Compact head-mounted display system

ABSTRACT

There is provided a method for fabricating an optical device having a light wave transmitting substrate with at least two major surfaces and edges, input and output reflecting surfaces carried by the substrate, for producing a substrate allowing light waves to traverse the substrate between the two major surfaces, the method including attaching to each other a plurality of substantially transparent flat plates arranged in a stack, slicing the stack to form a substrate with two major surfaces, and coupling-in and coupling-out reflecting surfaces, with major surfaces being parallel to each other and not parallel to the input or the output surfaces, grinding or polishing the substrate, and cutting the substrate to final dimensions.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.15/999,300, filed Aug. 17, 2018 for “COMPACT HEAD-MOUNTED DISPLAYSYSTEM”, which is hereby incorporated by reference herein.

FIELD OF THE INVENTION

The present invention relates to substrate light waves guided opticaldevices, and particularly to devices which include a reflecting surfacecarried by a light-transmissive substrate.

The invention can be implemented to advantage in a large number ofimaging applications, such as, head-mounted and head-up displays,cellular phones, compact displays, 3-D displays, compact beam expanders,as well as non-imaging applications such as flat-panel indicators,compact illuminators and scanners.

BACKGROUND OF THE INVENTION

One of the important applications for compact optical elements is inhead-mounted displays (HMDs), wherein an optical module serves both asan imaging lens and a combiner, in which a two-dimensional display isimaged to infinity and reflected into the eye of an observer. Thedisplay can be obtained directly from either a spatial light modulator(SLM), such as a cathode ray tube (CRT), a liquid crystal display (LCD),an organic light emitting diode array (OLED), or a scanning source andsimilar devices, or indirectly, by means of a relay lens, or an opticalfiber bundle. The display comprises an array of elements (pixels) imagedto infinity by a collimating lens and transmitted into the eye of theviewer by means of a reflecting or partially reflecting surface actingas a combiner for non-see-through and see-through applications,respectively. Typically, a conventional, free-space optical module isused for these purposes. As the desired field-of-view (FOV) of thesystem increases, such a conventional optical module becomes larger,heavier and bulkier, and therefore, even for a moderate performancedevice, is impractical. This is a major drawback for all kinds ofdisplays but especially in head-mounted applications, wherein the systemshould be as light and compact as possible.

The strive for compactness has led to several different complex opticalsolutions, all of which, on the one hand, are still not sufficientlycompact for most practical applications, and on the other hand, suffermajor drawbacks in terms of manufacturability. Furthermore, theeye-motion-box (EMB) of the optical viewing angles resulting from thesedesigns is usually very small—typically less than 8 mm. Hence, theperformance of the optical system is very sensitive, even for smallmovements of the optical system relative to the eye of the viewer, anddo not allow sufficient pupil motion for conveniently reading text fromsuch displays.

DISCLOSURE OF THE INVENTION

The present invention facilitates the provision of compact substratesfor, amongst other applications, HMDs. The invention allows relativelywide FOVs together with relatively large EMB values. The resultingoptical system offers a large, high-quality image, which alsoaccommodates large movements of the eye. The optical system offered bythe present invention is particularly advantageous because it issubstantially more compact than state-of-the-art implementations, andyet it can be readily incorporated, even into optical systems havingspecialized configurations.

A further application of the present invention is to provide a compactdisplay with a wide FOV for mobile, hand-held applications such ascellular phones. In today's wireless internet-access market, sufficientbandwidth is available for full video transmission. The limiting factorremains the quality of the display within the device of the end-user.The mobility requirement restricts the physical size of the displays,and the result is a direct-display with poor image viewing quality. Thepresent invention enables a physically compact display with a largevirtual image. This is a key feature in mobile communications, andespecially for mobile internet access, solving one of the mainlimitations for its practical implementation. Thereby the presentinvention enables the viewing of digital content of a full formatinternet page within a small, hand-held device, such as a cellularphone.

A broad object of the present invention is, therefore, to alleviate thedrawbacks of state-of-the-art compact optical display devices and toprovide other optical components and systems having improvedperformance, according to specific requirements.

In accordance with the present invention there is therefore provided amethod for fabricating an optical device having a light wavetransmitting substrate with at least two major surfaces and edges, inputand output reflecting surfaces carried by the substrate for producing asubstrate allowing light waves to traverse the substrate between the twomajor surfaces, the method comprising attaching to each other aplurality of substantially transparent flat plates arranged in a stack,slicing the stack to form a substrate with two major surfaces andcoupling-in and coupling-out reflecting surfaces with major surfacesbeing parallel to each other and not parallel to the input or the outputsurfaces, grinding or polishing the substrate and cutting the substrateto final dimensions.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is described in connection with certain preferredembodiments, with reference to the following illustrative figures sothat it may be more fully understood.

With specific reference to the figures in detail, it is stressed thatthe particulars shown are by way of example and for purposes ofillustrative discussion of the preferred embodiments of the presentinvention only, and are presented to provide what is believed to be themost useful and readily understood description of the principles andconceptual aspects of the invention. In this regard, no attempt is madeto show structural details of the invention in more detail than isnecessary for a fundamental understanding of the invention. Thedescription taken with the drawings are to serve as direction to thoseskilled in the art as to how the several forms of the invention may beembodied in practice.

In the drawings:

FIG. 1 is a side view of an exemplary prior art light-guide opticalelement;

FIGS. 2A and 2B are diagrams illustrating detailed sectional views of anexemplary prior art array of selectively reflective surfaces;

FIG. 3 is a schematic sectional-view of a prior art reflective surfacewith two different impinging rays;

FIGS. 4A and 4B illustrate sectional views of a transparent substratehaving coupling-in and coupling-out surfaces, according to the presentinvention;

FIGS. 5A, 5B, 5C and 5D are schematic sectional-views of foldingreflecting surfaces which re-direct the coupled-out light waves into theviewer's eye, according to the present invention;

FIG. 6 is a graph illustrating the reflection of incident light waves onan interface plane as a function of the incident angle, according to thepresent invention;

FIG. 7 is a graph illustrating the reflection of incident light waves onthe coupling-out reflecting surface as a function of the incident angle,according to the present invention;

FIGS. 8A, 8B and 8C illustrate sectional views of optical modules inwhich correcting lenses are attached to the main transparent substrate,according to the present invention;

FIGS. 9A, 9B, 9C and 9D illustrate sectional views of non-active partsof the coupling-out surfaces and methods to block it (9A-9C), oralternately, to utilize it (9D), according to the present invention;

FIGS. 10A and 10B illustrate sectional views of transparent substrates,where two light rays coupled into the substrate remotely separated fromeach other are, coupled-out adjacent to each other, according to thepresent invention;

FIGS. 11A, 11B, 11C and 11D are schematic sectional-views of opticaldevices in which two different transparent substrates are opticallyattached together, according to the present invention;

FIGS. 12A, 12B, 12C and 12D are schematic sectional-views of opticaldevices in which an angular sensitive reflecting surface is embeddedinside the transparent substrate, according to the present invention;

FIG. 13 is a graph illustrating the reflection of the incident lightwaves on an angular sensitive reflecting surface as a function of theincident angle, according to the present invention;

FIG. 14 is another graph illustrating the reflection of the incidentlight waves on an angular sensitive reflecting surface as a function ofthe incident angle, according to the present invention;

FIGS. 15A and 15B schematically illustrate various ways to couple lightwaves into the transparent substrate using a transparent prism attachedto one of the external surfaces of the substrate, according to thepresent invention;

FIGS. 16A, 16B and 16C schematically illustrate various ways to mix thecoupled light waves inside the substrate by optically cementing a thintransparent plate to one of the major surfaces of the substrate,according to the present invention;

FIG. 17 is a graph illustrating the reflection of incident light waveson an interface plane between a thin transparent plate and a majorsurface of the substrate as a function of the incident angle, accordingto the present invention;

FIGS. 18A, 18B and 18C are schematic sectional-views of optical devicesin which two different transparent substrates are optically attachedtogether and one of the coupling-in elements is an angular sensitivereflecting surface, according to the present invention;

FIG. 19 schematically illustrates the active parts of the coupling-outsurface according to the viewing angle and the eye-motion-box of thesystem;

FIGS. 20A, 20B, and 20C are schematic sectional-views of optical devicesin which four different transparent substrates are optically attachedand two of the coupling-in elements are angular sensitive reflectingsurfaces, according to the present invention;

FIGS. 21A and 21B are graphs illustrating the reflection of incidentlight waves on two different angular sensitive coupling-in surfaces as afunction of the incident angle according to the present invention;

FIG. 22 schematically illustrates active parts of a coupling-out surfaceaccording to the viewing angle and the eye-motion-box of the system,wherein at least part of the coupling-in elements are angular sensitivereflecting surfaces;

FIGS. 23A, 23B and 23C are schematic sectional-views of optical devicesin which a reflecting surface is embedded inside the transparentsubstrate and the output aperture of the system is expanded, accordingto the present invention;

FIG. 24 is a graph illustrating the reflection of incident light waveson a partially reflecting surface as a function of an incident angle,according to the present invention;

FIGS. 25A, 25B and 25C are other schematic sectional-views of foldingreflecting surfaces which re-direct the coupled-out light waves into theviewer's eye, according to the present invention;

FIG. 26 is a diagram illustrating exploiting more than two propagationorders of the coupled light waves inside the substrate, according to thepresent invention;

FIG. 27 is a diagram illustrating a method for fabricating the requiredtransparent substrate according to the present invention, and

FIGS. 28A, 28B, 28C, 28D and 28E are diagrams illustrating a method forfabricating a transparent substrate, according to the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 1 illustrates a sectional view of a prior art light-guide opticalelement. The first reflecting surface 16 is illuminated by a plane lightwave 18 emanating from a display source 4 and collimated by a lens 6,located behind the device. The reflecting surface 16 reflects theincident light from the source, such that the light is trapped inside aplanar substrate 20 by total internal reflection. After severalreflections off the major surfaces 26, 27 of the substrate, the trappedlight waves reach an array of partially reflecting surfaces 22, whichcouple the light out of the substrate into an eye 24, having a pupil 25,of a viewer. Assuming that the central light wave of the source iscoupled out of the substrate 20 in a direction normal to the substratesurface 26, the partially reflecting surfaces 22 are flat, and theoff-axis angle of the coupled light wave inside the substrate 20 isα_(in), then the angle α_(sur2) between the reflecting surfaces and themajor surfaces of the substrate is:

$\begin{matrix}{\alpha_{{sur}\; 2} = {\frac{\alpha_{in}}{2}.}} & (1)\end{matrix}$

As can be seen in FIG. 1, the trapped rays arrive at the reflectingsurfaces from two distinct directions 28, 30. In this particularembodiment, the trapped rays arrive at the partially reflecting surface22 from one of these directions 28 after an even number of reflectionsfrom the substrate major surfaces 26 and 27, wherein the incident angleβ_(ref) between the trapped ray and the normal to the reflecting surfaceis:

$\begin{matrix}{\beta_{ref} = {{\alpha_{in} - \alpha_{{sur}\; 2}} = {\frac{\alpha_{in}}{2}.}}} & (2)\end{matrix}$

The trapped rays arrive at the partially reflecting surface 22 from thesecond direction 30 after an odd number of reflections from thesubstrate surfaces 26 and 27, where the off-axis angle isα′_(in)=−α_(in) and the incident angle between the trapped ray and thenormal to the reflecting surface is:

$\begin{matrix}{{\beta_{ref}^{\prime} = {{\alpha_{in}^{\prime} - \alpha_{{sur}\; 2}} = {{{- \alpha_{in}} - \alpha_{{sur}\; 2}} = {- \frac{3\;\alpha_{in}}{2}}}}},} & (3)\end{matrix}$where, the minus sign denotes that the trapped ray impinges on the otherside of the partially reflecting surface 22. As further illustrated inFIG. 1, for each reflecting surface, each ray first arrives at thesurface from the direction 30, wherein some of the rays again impinge onthe surface from direction 28. In order to prevent undesired reflectionsand ghost images, it is important that the reflectance be negligible forthe rays that impinge on the surface having the second direction 28.

An important issue to be considered is the actual active area of eachreflecting surface. A potential non-uniformity in the resulting imagemight occur due to the different reflection sequences of different raysthat reach each selectively reflecting surface: some rays arrive withoutprevious interaction with a selectively reflecting surface and otherrays arrive after one or more partial reflections. This effect isillustrated in FIG. 2A. Assuming that for example α_(in)=50°, the ray 31intersects the first partially reflecting surface 22 at the point 32.The incident angle of the ray is 25° and a portion of the ray's energyis coupled out of the substrate. The ray then intersects the samepartially reflecting surface at point 34 at an incident angle of 75°,without a noticeable reflection, and then intersects again at point 36with an incident angle of 25°, where another portion of the energy ofthe ray is coupled out of the substrate. In contrast, the ray 38 shownin FIG. 2B undergoes only one reflection 40 from the same surface.Further multiple reflections occur at other partially reflectingsurfaces.

FIG. 3 illustrates this non-uniformity phenomenon with a detailedsectional view of the partially reflective surface 22, which coupleslight trapped inside the substrate out and into the eye 24 of a viewer.As can be seen, the ray 31 is reflected off the upper surface 27, nextto the line 50, which is the intersection of the reflecting surface 22with the upper surface 27. Since this ray does not impinge on thereflecting surface 22, its brightness remains the same and its firstincidence at surface 22 is at the point 52, after double reflection fromboth external surfaces. At this point, the light wave is partiallyreflected and the ray 54 is coupled out of the substrate. For otherrays, such as ray 38, which is located just below ray 31, the firstincidence at surface 22 is at point 56, before it meets the uppersurface 27, wherein the light wave is partially reflected and the ray 58is coupled out of the substrate. Hence, when it impinges on surface 22at point 60, following double reflection from the external surfaces 26,27, the brightness of the coupled-out ray is lower than the adjacent ray54. As a result, all the coupled-out light rays with the same coupled-inangle as 31 that arrive at surface 22 left of the point 52, have a lowerbrightness. Consequently, the reflectance from surface 22 is actually“darker” left of the point 52 for this particular couple-in angle.

It is difficult to fully compensate for such differences inmultiple-intersection effects. Nevertheless, in practice, the human eyetolerates significant variations in brightness, which remains unnoticed.For near-to-eye displays, the eye integrates the light which emergesfrom a single viewing angle and focuses it onto one point on the retina,and since the response curve of the eye is logarithmic, smallvariations, if any, in the brightness of the display will not benoticeable. Therefore, even for moderate levels of illuminationuniformity within the display, the human eye experiences a high-qualityimage. The required moderate uniformity can readily be achieved with theelement illustrated in FIG. 1. For systems having large FOVs, and wherea large EMB is required, a comparatively large number of partiallyreflecting surfaces is needed to achieve the desired output aperture. Asa result, the non-uniformity due to the multiple intersections with thelarge number of partially reflecting surfaces becomes more dominant,especially for displays located at a distance from the eye, such asHUDs, and the non-uniformity cannot be tolerated. For these cases, amore systematic method for overcoming the non-uniformity is required.

Since the “darker” portions of the partially reflecting surfaces 22contribute less to the coupling of the trapped light waves out of thesubstrate, their impact on the optical performance of the substrate canbe only negative, namely, there will be darker portions in the outputaperture of the system and dark stripes will exist in the image. Thetransparency of each one of the reflecting surfaces is, however, uniformwith respect to the light waves from the external scene. Therefore, ifoverlapping is set between the partially reflective surfaces tocompensate for the darker portions in the output aperture, then raysfrom the output scene that cross these overlapped areas will suffer fromdouble attenuations and darker stripes will be created in the externalscene. This phenomenon significantly reduces the performance not only ofdisplays which are located at a distance from the eye, such as head-updisplays, but also that of near-eye displays, and hence, it cannot beutilized.

FIGS. 4A and 4B illustrate embodiments for overcoming theabove-described problem, according to the present invention. Instead ofpartially overcoming the undesired secondary reflections from thepartially reflecting surfaces, these reflections are utilized to expandthe output aperture of the optical system. As illustrated in FIG. 4A,two rays 63 from a plane light waves emanating from a display source andcollimated by a lens (not shown) enter a light transparent substrate 64,having two parallel major surfaces 70 and 72, at an incident angle ofα_(in) ⁽⁰⁾ in respect to axis 61, which is normal to the major surfaces70, 72 of the substrate. The rays impinge on the reflecting surface 65which is inclined at an angle α_(sur1) to the major surfaces of thesubstrate. The reflecting surface 65 reflects the incident light rayssuch that the light rays are trapped inside a planar substrate 64 bytotal internal reflection from the major surfaces. The off-axis angleα_(in) ⁽¹⁾ between the trapped ray and the normal to the major surfaces70, 72 isα_(in) ⁽¹⁾=α_(in) ⁽⁰⁾+2·α_(sur1).  (4)

After several reflections off the surfaces of the substrate, the trappedlight rays reach a second flat reflecting surface 67, which couples thelight rays out of the substrate. Assuming that surface 67 is inclined atthe same angle to the major surfaces as the first surface 65, that is tosay, surfaces 65 and 67 are parallel and α_(sur2)=α_(sur1), then theangle α_(out) between the coupled out rays and the normal to thesubstrate plane isα_(out)=α_(in) ⁽¹⁾−2·α_(sur2)=α_(in) ⁽¹⁾−2·α_(sur1)=α_(in) ⁽⁰⁾.  (5)

That is to say, the coupled-out light rays are inclined to the substrateat the same angle as the incident light rays. So far, the coupled-inlight waves behave similar to the light waves illustrated in the priorart of FIG. 1. FIG. 4B, however, illustrates, a different behaviorwherein two light rays 68, having the same incident angle of α_(in) ⁽⁰⁾as rays 63, impinge on points 69 which are located at the right side ofthe reflecting surface 65. After a first reflection from surfaces 65,when the coupled light rays are trapped inside the substrate at anoff-axis angle of α_(in) ⁽¹⁾, the light rays are reflected from theupper major surface 70, and impinge again on points 71 at surface 65.The light rays are reflected again from surface 65 and the off-axisangle of the trapped rays inside the substrate is nowα_(in) ⁽²⁾=α_(in) ⁽¹⁾+2·α_(sur1)=α_(in) ⁽⁰⁾+4·α_(sur1).  (6)

After several reflections off the surfaces of the substrate, the trappedlight rays reach the second reflecting surface 67. The light rays 68first impinge on points 74 which are located at the right side (which ispractically an active side) of the reflecting surface 67. After a firstreflection from surfaces 67, when the coupled light rays are stilltrapped inside the substrate at an off-axis angle of α_(in) ⁽¹⁾, thelight rays are reflected from the lower major surface 72 and impingeagain on points 76 located at the right side of the reflecting surface67. The light rays are then reflected again, and the off-axis angle ofthe light rays is now:α_(out)=α_(in) ⁽²⁾−4·α_(sur1)=α_(in) ⁽¹⁾−2·α_(sur1)==α_(in) ⁽⁰⁾.  (7)

That is to say, the light rays 68, which are reflected twice from thecoupling-in reflecting surface 65, as well as from the active side ofthe coupling-out surface 67, are coupled out from the substrate at thesame off-axis angle α_(out) as the other two rays 63 which are reflectedonly once from surfaced 65 and 67, which is also the same incident inputangle of these four rays on the substrate major planes.

As illustrated in FIGS. 4A and 4B, the optical element 64 of the presentinvention is differentiated from the prior art element 20 illustrated inFIGS. 1-3 by some prominent characteristics: first of all, differentrays emanating from the same input light waves (such as rays 63 and 68in FIGS. 4A and 4B) propagate inside the substrate having differentoff-axis angles (α_(in) ⁽¹⁾ and α_(in) ⁽²⁾, respectively). In addition,some of the trapped light rays impinge on the same side of thecoupling-out reflecting surface with two different incident angles andhave to be reflected at least twice from this surface in order to becoupled out from the substrate. As a result, proper notation rules mustbe defined in order to correctly note the various parameters of thetrapped light rays inside the substrate. For simplicity, from here onin, the refraction of the coupling-in or coupling-out light rays due tosecond Snell Law while entering or exiting the substrate is neglected,and it is assumed that the materials of the optical elements which arelocated next to the substrate's surfaces, are similar to that of thesubstrate. The element should be separated by an air gap or by anadhesive having lower refractive index, in order to enable the totalinternal reflection of the trapped rays inside the substrate. In anycase, only the directions of the rays inside the substrate areconsidered. In order to differentiate between the various “propagationorders” of the trapped light waves, a superscript (i) will denote theorder i. The input light waves which impinge on the substrate in thezero order are denoted by the superscript (0). After each reflectionfrom the coupling-in reflecting surface the order of the trapped ray isincreased by one from (i) to (i+1) whereα_(in) ^((i+1))=α_(in) ^((i))+2·α_(sur1).  (8)Similarly, after each reflection from the coupling-out reflectingsurface the order of the trapped ray is decreased by one from (i) to(i−1) whereα_(in) ^((i−1))=α_(in) ^((i))−2·α_(sur2).  (9)The angular spectrum of light waves which are located in a given orderare confined by the two extreme angles of these order, that is:α_(n) ^((i))(min)<α_(in) ^((i))<α_(in) ^((i))(max),  (10)where, α_(in) ^((i))(min) and α_(in) ^((i))(max) are the minimal and themaximal angles of the order (i), respectively. The direction of thecentral light wave of the image is:

$\begin{matrix}{{{\alpha_{in}^{(1)}({cen})} = \frac{{\alpha_{in}^{(i)}( \max )} + {\alpha_{in}^{(i)}( \min )}}{2}},} & (11)\end{matrix}$The FOV of the image inside the substrate is:FOV=α_(in) ^((i))(max)−α_(in) ^((i))(min),  (12)The FOV inside the substrate does not depend on the order (i). Theentire angular spectrum of the light waves which are located in a givenorder (i) are denoted byF ^((i))≡{α_(in) ^((i))(min),α_(in) ^((i))(max)},  (13)whereF ^((i+1)) =F ^((i))+2·α_(sur1).  (14)The incident angles of the light rays on the coupling-in andcoupling-out reflecting surfaces are also can be denotes as α_(si)^((i)) and α_(so) ^((i)), respectively, whereα_(si) ^((i))=α_(in) ^((i))+α_(sur1)  (15)andα_(so) ^((i))=α_(in) ^((i))−α_(sur2).  (16)

It is apparent from Eqs. (5) and (7) that in order for the outputdirection of different rays which undergo different number ofreflections from the reflecting surfaces to be the same, the tworeflecting surfaces should be strictly parallel to each other. Inaddition, any deviation between the incident angles of the trapped lightrays on the two major surfaces will cause, at each reflecting cycle, adrift in the off-axis angle α_(in) ^((i)). Since the trapped light raysfrom the higher order undergo a much smaller number of reflections fromthe major surfaces of the substrate than those from the lower order, thedrift of the low order will be much more noticeable than that of thehigh order. As a result, it is required that the parallelism between themajor surfaces of the substrate will be achieved to a high degree.

In order that the light waves will be coupled into the substrate 64 bytotal internal reflection, it is necessary that for the entire FOV ofthe image the off-axis angle inside the substrate will fulfill theequationα_(in) ⁽¹⁾>α_(cr),  (17)where, α_(cr) is the critical angle for total internal reflection insidethe substrate. On the other hand, in order for the light waves to becoupled out from the substrate, it is necessary that the entire FOV ofthe image the off-axis angle of the output light waves will fulfill theequation:α_(in) ⁽⁰⁾<α_(cr).  (18)Combining Eqs. (9), (11), (12) and (17) yields

$\begin{matrix}{{\alpha_{in}^{(0)}({cen})} = {{{\alpha_{in}^{(1)}( \min )} + \frac{FOV}{2} - {2 \cdot \alpha_{{sur}\; 2}}} > {\alpha_{cr} + \frac{FOV}{2} - {2 \cdot {\alpha_{{sur}\; 2}.}}}}} & (19)\end{matrix}$In order for the entire first two orders to be coupled inside thesubstrate the conditionα_(in) ⁽²⁾(max)<90°−α_(sur2)  (20)must be fulfilled. In addition, even for material having an extremelyhigh refractive index, and even where the external media which isadjacent to major surfaces of the substrate is air, the critical angleis limited byα_(cr)>32°.  (21)Combining Eqs. (9), (12), (18), (20) and (21) yields3α_(sur2)<90°−FOV−α_(cr),  (22)which yields, even for moderate FOV of 10° inside the substrate, thelimitation of:α_(sur2)<16°  (23)Combining Eqs. (19), (21) and (23) yields, the limitation of:α_(in) ⁽⁰⁾(cen)>5°⇒α_(out) ⁽⁰⁾(cen)>9°,  (24)wherein, α_(out) ⁽⁰⁾(cen) is the inclined output angle in the air,namely, the coupled-out image is substantially inclined in relation tothe normal to the substrate plane. For wider FOVs and smaller α_(sur2),the inclination angle will be increased. Usually however, it is requiredthat the coupled-out image, which is projected to the viewer's eye, willbe oriented substantially normal to the substrate plane.

As illustrated in FIG. 5A, the inclination of the image can be adjustedby adding a partially reflecting surface 79 which is inclined at anangle of

$\frac{\alpha_{in}^{(0)}({cen})}{2}$to the surface 72 of the substrate. As shown, the image is reflected androtated such that it passes again through the substrate substantiallynormal to the substrate major surfaces. As illustrated in FIG. 5B, inorder to minimize distortion and chromatic aberrations, it is preferredto embed surface 79 in a prism 80, and to complete the shape of thesubstrate 64 with a second prism 82, both of them fabricated of amaterial similar to that of the substrate. In order to minimize thethickness of the system it is possible, as illustrated in FIG. 5C, toreplace the single reflecting surface 80 with as array of parallelpartially reflecting surfaces 79 a, 79 b, etc., where the number of thepartially reflecting surfaces can be determined according to therequirements of the system.

There are two contradicting requirements from the interface plane 83(FIG. 5D) between the substrate 64 and the prism 80. On the one hand,the first order image F⁽¹⁾ should be reflected from that plane, whilethe zero order image F⁽⁰⁾ should substantially pass through it, afterbeing reflected from surface 67, with no significant reflections. Inaddition, as illustrated in FIGS. 5A-5C, after being reflected fromsurface 79, the optical wave passes again through the interface plane 83and here also it is required that the undesired reflections will beminimized. A possible way to achieve it this, as illustrated in FIG. 5D,is to use an air gap in the interface plane 83. It is preferred,however, in order to achieve a rigid system, to apply an opticaladhesive in the interface plane 83, in order to cement the prism 80 withthe substrate 64. This approach is illustrated hereby with an opticalsystem having the following parameters:α_(sur1)=α_(sur2)=10°; F ⁽⁰⁾={30°,40°}; F ⁽¹⁾={50°,60°} F⁽²⁾={70°,80°}.  (25)The light waves are s-polarized. The optical material of the substrate64 and the prisms 80 and 82 is Schott N-SF57 having a refractive indexof n_(d)=1.8467, and the optical adhesive is NOA 1315, having arefractive index of n_(d)=1.315. The critical angle is thereforeα_(cr)>45.4°. All the optical rays in the higher orders F⁽¹⁾ and F⁽²⁾have off-axis angles higher than the critical angle, and therefore, theyare totally reflected from the interface plane 83. All the optical raysin the zero order impinge on the interface plane at an incident anglelower than the critical angle, and hence, they pass through it. Tominimize the Fresnel reflections of the coupled-out light waves from theinterface plane, however, it is preferred to apply a suitableanti-reflective (AR) coating to this plane.

FIG. 6 illustrates the graph of the reflection from the interface planecoated with an appropriate AR coating as a function of the incidentangle for three different wavelengths: 450 nm, 550 nm and 650 nm, whichpractically cover the relevant photopic region. As shown, the reflectionis 100% for the angular spectrum above 45°, while it is below 3% for theincident angles {30°, 40°} of the zero order, as well as for the lightwaves which pass again substantially normal to the plane 83 after beingreflected from surface 79.

Another requirement is that surface 67 will be reflective for theincident angles of) the higher orders α_(so) ⁽¹⁾ and α_(so) ⁽²⁾, as wellas transparent for the coupled-out light waves which pass through thisplane after being coupled out from the substrate, reflected by surface79, and pass again through the interface plane 83. That is, for theexemplified system given above, the surface should be reflective forincident angles above 40° and substantially transparent for incidentangles below 15°. Here also an air gap between surface 67 and prism 82is a possible solution, but here again it is preferred to cement theelement together with an optical adhesive. The requirements from thedielectric coating that should be applied to the surface 67 is thereforeto be reflective for the incident angles of 40°<α_(so) ⁽¹⁾<45° (above45° the light rays are totally reflected from the surface), andsubstantially transparent for the incident angles below 15°.

FIG. 7 illustrates the graph of the reflection from the interface planecoated with an appropriate angular sensitive coating as a function ofthe incident angle for three different wavelengths: 450 nm, 550 nm and650 nm. As shown, the reflection is higher than 93% for the angularspectrum between 40° and 45°, while it is below 2% for the incidentangles below 15° as required.

Concerning the reflectance of surface 79, this parameter depends on thenature of the optical system. In non-see-through systems, such asvirtual-reality displays, the substrate can be opaque, and thetransmittance of the system has no importance. In that case, it ispossible to apply a simple highly reflecting coating, either metallic ordielectric, on the surface. In that case, since on the one hand thereflection of surfaces 65 and 79 is very high for the impinging lightwaves and on the other hand the reflection of surfaces 67 and 83 is veryhigh for the light waves that should be reflected from them and very lowfor light waves that should be transmitted through them, the totalefficiency of the optical system can be high. In see-through systems,such as HMDs for military or professional applications, or for augmentedreality systems, wherein the viewer should see the external scenethrough the substrate, surface 79 should be at least partiallytransparent. As a result, in such a case a partially reflecting coatingshould be applied to surface 79. The exact ratio between thetransmission and the reflection of the coating should be determinedaccording to the various requirements of the optical system. In theevent that an array of partially reflecting surfaces 79 a, 79 b . . . isused to reflect the light waves to a viewer's eye, the reflectance ofthe coating should be the same for all the partially reflecting surfacesin order to project a uniform image to the viewer's eye as well as totransmit a uniform external seen.

In all of the embodiments of the invention described hereinabove, theimage transmitted by the substrate is focused to infinity. However,there are applications or uses where the transmitted image should befocused to a closer distance, for example, for people who suffer frommyopia and cannot properly see images located at long distances. FIG. 8Aillustrates an embodiment for implementing a lens, based on the presentinvention. A collimated image 84 is coupled into the substrate 64 by thereflecting surface 65, reflected (once or twice, depending on the orderof the coupled rays) by the angular selective reflecting surface 67,passes through the interface plane 83, is partially reflected by thearray of partially reflecting surfaces 79 a, 79 b, and passes againthrough surface 83 into the eye 24 of a viewer. The ophthalmicplano-concave lens 86, which is attached to the upper surface 70 of thesubstrate, focuses the images to a convenient distance, and optionallycorrects other aberrations of the viewer's eye, including astigmatism.Since the lens 86 is attached to prism 82, which is not active in themechanism for trapping of the optical waves inside the substrate 64 bytotal internal reflection, a simple cementing procedure can be used tooptically attach the lens 86 to prism 82. There are applications,however, such as illustrated in FIG. 8B, where the lens 86 should havean extended aperture, and hence, it should also be attached to the uppersurface 70 of the substrate. Here, since this surface is active intrapping the light waves inside the substrate, an isolation layer shouldbe provided in the interface plane 85 between the lens and thesubstrate, to ensure the trapping of the image rays inside the substrateby a total internal reflection. A possible way to achieve this is to usean air gap in the interface plane 85. It is preferred, however, asexplained above, to apply an optical adhesive in the interface plane, inorder to cement the prism 82 with the lens 86. As illustrated above inrelation to FIG. 6, an appropriate AR coating can be applied to theinterface plane 85, in order to minimize the Fresnel reflections fromthis plane.

In all of the embodiments of the invention described above, it isassumed that the external scene is located at infinity. There arehowever applications, such as for professional or medical staff, wherethe external scene is located at closer distances. FIG. 8C illustrates asystem for implementing a dual lens configuration, based on the presentinvention. A collimated image 84 is coupled into the substrate 64 by thereflecting surface 65, reflected by the angular selective reflectingsurface 67, passes through the interface plane 83, is partiallyreflected by the array of partially reflecting surfaces 79 a, 79 b . . .and passes again through surface 83 into the eye 24 of a viewer. Anotherscene image 90 from a close distance is collimated to infinity by a lens89, and then passed through the substrate 64 into the eye. The lens 86focuses the images 84 and 90 to a convenient distance, usually theoriginal distance of the external scene 90, and corrects otheraberrations of the viewer's eye, if required. Since the lower surface 81of prism 80 is not active with regard to the optical waves that arecoupled inside the substrate 64 by total internal reflection anddirected by the reflecting surface 79 into the viewer's eye, it ispossible to optically attach a prism 80 with a lens 89 using aconventional cementing procedure.

The lenses 86 and 89 plotted in FIGS. 8A-8C are simple plano-concave andplano-convex lenses, respectively. To keep the planar shape of thesubstrate, it is possible, however, to instead utilize Fresnel lenses,which can be made of thin molded plastic plates with fine steps.Moreover, an alternative way for realizing the lenses 86 or 89, insteadof as fixed lenses as described above, is to use electronicallycontrolled dynamic lenses. There are applications where it is requiredthat the user will be able not only to see a non-collimated image, butalso to dynamically control the focus of the image. Recently, it hasbeen shown that a high resolution, spatial light modulator (SLM) can beused to form a dynamic focusing element. Presently, the most popularsources for that purpose are LCD devices, but other dynamic SLM devicescan be used as well. High resolution, dynamic lenses having severalhundred lines/mm are known. This kind of electro-optically controlledlenses can be used as the desired dynamic elements in the presentinvention, instead of the fixed lenses described above in conjunctionwith FIGS. 8A-8C. Therefore, the operator can determine and set, in realtime, the exact focal planes of both the virtual image projected by thesubstrate 64 as well as the real image of the external view.

The embodiment of the present invention illustrated in FIGS. 4-8 hasseveral significant advantages as compared to the embodiment of theprior art illustrated in FIGS. 1-3. The main reason for this is thatbecause of the small angle of α_(sur2), the active area of the outputaperture of the substrate having a single reflecting surface 67, is muchlarger than that of a substrate having a single coupling-out partiallyreflecting surface which is based on the prior art technology. Forexample, a substrate with a single reflecting surface 67 having aninclination angle of α_(sur2)=10° has an output aperture that willrequire at least 3-4 facets for a substrate of the prior art technologywith a same thickness having an inclination angle of α_(sur2)˜30°. As aresult, the fabrication process of the substrate will be much simplerthan that of the prior art. In addition, since for many applicationsonly a single facet is needed to achieve the required output aperture,the projected image can be much smoother and with higher optical qualitythan that of the multi-facet element of the prior art. There are,however, some considerations that should be taken into an accountconcerning the output and the input apertures of the optical device ofthe present invention.

Regarding the output aperture as illustrated in FIG. 9A, a ghost imageproblem might be accrued at the edge of the reflecting surface 67. Asshown, a ray 91 having an off-axis angle α_(in) ⁽⁰⁾ is traced from theoutput aperture backward to the input aperture of the substrate 64. Theray 91 impinges on the reflecting surface at point 93 a and is reflectednot only twice, but rather three times from the reflecting surface 67.As a result, the ray is trapped inside the substrate 64 having anoff-axis angle α_(in) ⁽³⁾, which is located in the third order of thecoupled-in light waves. As illustrated in FIG. 9A, this angle fulfilsthe relation α_(in) ⁽³⁾>90°−α_(sur2), and as a result, it is not a“legal” angle. As seen, the ray 91 is reflected from the third point 93c not toward the lower major surface 72 but toward the upper surface 70.Therefore, ray 91 will impinge on surface 72 at the angleα_(in) ⁽³⁾(act)=180°−α_(in) ⁽³⁾=180°−2·α_(sur2)−α_(in) ⁽²⁾.  (26)As a result, after an odd number of reflections from the major surfacesthe ray will be reflected from the input surface 65 at the angleα_(in) ⁽²⁾(act)=α_(in) ⁽³⁾(act)−2·α_(sur2)=180°−4·α_(sur2)−α_(in)⁽²⁾.  (27)Consequentlyα_(in) ⁽⁰⁾(act)=α_(in) ⁽²⁾(act)−4·α_(sur2)=180°−12·α_(sur2)−α_(in)⁽⁰⁾.  (28)

Evidently, this angle in not necessarily the required angle α_(in) ⁽⁰⁾.Using, for example, the parameters of the example given above inrelation to Eq. (23), and assuming that α_(in) ⁽⁰⁾=31°, the actual raythat is coupled into the substrate 64, in order to be coupled-out as ray91, has the direction of α_(in) ⁽⁰⁾(act)=29°. That is to say, not onlyis the “right” ray that should be coupled out as ray 91 missing from theimage, and consequently, a gap will be formed in the image, but insteadthere is another ray originated from a “wrong” direction, which createsa ghost image.

A possible way to overcome this problem is illustrated in FIG. 9B. Asshown, a flat transparent plate 95 is cemented to the lower surface 72of the substrate 64 defining an interface plane 96. The ray 91 isreflected now only twice from surface 67 before being coupled into thesubstrate 64. Therefore, the coupled ray 97 propagates inside thesubstrate is having an off-axis angle α_(in) ⁽²⁾ which is a “legal”direction, and no ghost image is created in the image. In a case whereit is required to minimize the Fresnel reflections of the coupled ray 97at points 98 from the interface plane 96, it will be preferred to useoptical cement having a refractive index similar to that of thesubstrate 64 and plate 95.

An alternative manner of overcoming the ghost image problem isillustrated in FIG. 9C. Here, the reflecting surface 79 is shiftedinside the prism 80 such that it does not cover the entire aperture ofthe reflecting surface 67. That is to say, the rays that are reflectedat the far edge by segment 99 of the reflecting surface 67 are notreflected back to the viewer's eye by surface 79. As a result, part ofsurface 67 is practically blocked from being active and the segment 99becomes non-active. Therefore, the ray 91 having the “wrong” directiondoes not illuminates the viewer's eye and the ghost image is avoided.The exact parameters of the solution to the ghost image problem (if sameexists at all), such as which embodiment to use, or whether to use acombination thereof, the thickness of plate 95 or the shift of surface79 can be determined according to the various parameters of the opticalsystem such as the required measure of the output aperture, the FOV ofthe system and the desired overall thickness of the substrate.

Another alternative for overcoming the ghost image problem isillustrated in FIG. 9D. As illustrated here, the coupled ray 91 impingeson the lower major surface 72 before impinging on the reflecting surface65 having an off-axis angle α_(in) ⁽³⁾, namely, the same off-axis angleit has while reflected from surface 67 at the third point 93 c. As aresult, the coupled ray 91 is reflected three times from surface 65 atpoints 93 d, 93 e and 93 f before being coupled out from the substratehaving the off-axis angle α_(in) ⁽¹⁾, which is the “proper” angle. Inorder for the triple reflection from surface 67 to be compensated by atriple reflection from surface 65, it is necessary for the ray to bereflected the same number of reflections from the upper surface 70, aswell as from the lower surface 72, namely, if the ray is reflected fromsurface 67 upward toward surface 70, then it also should be reflectedfrom surface 72 upward toward surface 65. Usually, it is not possible todesign the optical system such that all the optical rays which arereflected three times from surface 67 will also be reflected three timesfrom surface 65. Only a small part of the rays which illuminate thesegment 99 (FIG. 9c ) of surface 67, and consequently, are reflectedthree times from surface 67, reach the EMB of the optical system.Usually, with a proper selection of the various parameters of theoptical system, such as the inclination angle of the reflecting surfaces65 and 67 and the thickness, the length and the refractive index of thesubstrate, it is possible to design the system such that for most of therelevant optical rays the triple reflection from surface 67 will becompensated by a triple reflection from surface 65 so that the ghostimages and the gaps in the image will be avoided.

Another issue that should be considered is the required measurement ofthe input aperture. In order to avoid gaps and stripes in the image itis desired that all the orders of the coupled-in light waves will fillthe substrate such that the reflecting surface 67 will be entirelyilluminated by the coupled-in light waves. As illustrated in FIG. 10A,to ensure this, the points on the boundary line 100 between the edge ofthe reflective surface 65 and the lower surface 72 of the substrate 64,should be illuminated for a single light wave by two different rays thatenter the substrate in two different locations: a ray 101 (dotted line)that illuminates directly surface 65 at the boundary line 100, andanother ray 102 (dashed line) which is first reflected by the reflectingsurface 65 at point 103 and then by the upper surface 70 of thesubstrate 64 before illuminating the lower surface 72 just left to theboundary line. As illustrated, the two rays 101 and 102 from the samepoint in the display source, which are propagated at the first orderinside the substrate, are coupled into the substrate 64 remotely locatedfrom each other: 101 at the left edge and 102 approximately at thecenter of surface 65, respectively. The rays are, however, coupled outby the coupling-out element 67 located adjacent to each other at theright part of surface 67. Therefore, the entire area of surface 65between points 103 and 100 should be illuminated by the light wave werethe rays 101 and 102 originated from. Consequently, this area should beentirely illuminated by all the light waves that are coupled into thesubstrate.

Similarly, as illustrated in FIG. 10B, the points on the boundary line100 between the edge of the reflective surface 65 and the lower surface72 should be illuminated for the same single light wave that illustratedabove in FIG. 10A, by two other different rays that enter the substratein two different locations: a ray 105 (dashed-dotted line) thatilluminates surface 65 at the boundary line 100 after one reflectionfrom surface 65 at a point located just right to 103 and one reflectionfrom surface 70, and another ray 106 (solid line) which is reflectedtwice by the reflecting surface 65 and twice by the upper surface 70 ofthe substrate 64 before illuminating the lower surface 72 just left tothe boundary line. As illustrated, the two rays 105 and 106 from thesame point in the display source, which are propagating at the secondorder inside the substrate, are coupled into the substrate 64 remotelylocated from each other: 105 approximately at the center and 106 closeto the right edge of surface 65, respectively. They are, however,coupled out by the coupling-out element 67 located adjacent to eachother at the left part of surface 67. Therefore, the entire area ofsurface 65 between points 103 and the right edge 104 of surface 65should be illuminated by the light wave, where the rays 105 and 106originated from. Consequently, this area should be entirely illuminatedby all the light waves that are coupled into the substrate. There aretwo conclusions from FIGS. 10A and 10B:

a. the entire area of surface 65 should be illuminated by light wavesthat are coupled into the substrate, and;

b. the first order of the coupled light waves illuminates the left partof surface 65 and is coupled out at the right part of surface 67, whilethe second order of the coupled light waves illuminates the right partof surface 65 and is coupled out at the left part of surface 67.

As illustrated in FIGS. 10A-10B, the aperture of the coupling-in surface65 is similar to that of the coupling-out surface 67. There are,however, systems having wide FOVs and large EMBs, and therefore, a largeoutput aperture is required. In addition, it is desired that the entireoptical system will be as compact as possible. Consequently, it isnecessary to minimize the input aperture of the substrate. As a result,there is a contradiction between the opposing requirements ofsimultaneously achieving a large output aperture along with a smallinput aperture. Therefore, an appropriate method should be found toreduce the input aperture for a given output aperture, or alternatively,to increase the output aperture for a given input aperture.

An embodiment for increasing the output aperture for a given inputaperture is illustrated in FIGS. 11A-11D. As shown in FIG. 11A, anoptical ray 107 having an input direction of α_(in) ⁽⁰⁾ impinges on anoptical element 109 composed of two substrates 110 a and 110 b, whereinthe lower surface 111 a of substrate 110 a is attached to the uppersurface 112 b of substrate 110 b defining an interface plane 117. Unlikethe substrates which are illustrated in FIGS. 4-10, the coupling-inelement 114 a of the upper substrate 110 a is not a simple reflectingsurface as surface 65 in substrate 64, but a partially reflectingsurface, meaning that the input ray 107 is split into two rays(preferably having the same brightness) 107 a and 107 b which arereflected from surfaces 114 a and 114 b and coupled inside substrates110 a and 110 b, respectively by total internal reflection. Unlikesurface 114 a, surface 114 b can be a simple reflecting surface. Asshown, rays 107 a and 107 b are reflected once from the left parts ofsurfaces 114 a and 114 b, respectively, and propagated inside thesubstrates in the first order having an angle of α_(in) ⁽¹⁾.Consequently, they are coupled out from the substrate by a singlereflection from the right parts of the coupling-out surfaces 116 a and116 b having an output angle of α_(in) ⁽⁰⁾. FIG. 11B illustrates thesame embodiment where now the input ray 107 impinges on the right sideof surfaces 114 a and 114 b. As a result, rays 107 a and 107 b arereflected twice from surfaces 114 a and 114 b, respectively, andpropagated inside the substrates in the second order having an angle ofα_(in) ⁽²⁾. Consequently, they are coupled out from the substrate by adouble reflection from the left parts of the coupling-out surfaces 116 aand 116 b having an output angle of α_(in) ⁽⁰⁾. As seen, surface 114 awhich is practically the input aperture of the optical device 109, hasapproximately half the size of the output aperture, which is practicallythe combination of the coupling-out surfaces 116 a and 116 b together.

There are two contradicting requirements from the interface plane 117between the substrates 110 a and 110 b. On the one hand, the first twoorders image F⁽¹⁾ and F⁽²⁾ should be reflected from that plane, whilethe zero order image F⁽⁰⁾ from the upper substrate 110 a shouldsubstantially pass through it, after being reflected from surface 116 a,with no significant reflections. Similarly, surface 117 should betransparent to ray 107 b that passes through surface 114 a having theinput angle of α_(in) ⁽⁰⁾. In addition, for see-through systems, thetransparency of optical device 109 for substantially normal incidentlight should be as high as possible. A possible way to achieve this isto use an air gap in the interface plane 117. An alternative manner forachieving this while maintaining the rigidness of the device, is tocement substrates 110 a and 110 b together using the same cementingmethod which utilizes low-index adhesive, as illustrated hereinabove inrelation to the interface plane 83 in FIG. 5D.

In the embodiment illustrated in FIGS. 11A-11B the two substrates 110 aand 110 b are similar to each other, i.e., the inclination anglesα_(sur1) of the coupling-in devices 114 a and 114 b, as well as theinclination angles α_(sur2) of the coupling-out devices 116 a and 116 b,are the same. In addition, the two substrates have the same thickness.It is possible, however, to attach two substrates having two differentcharacteristics. As illustrated in FIG. 11C, the upper substrate 110 ahas the same parameters as the system illustrated above in relation toEq. (23). The lower substrate however has the following parameters:α_(sur1)=α_(sur2)=11°; F ⁽⁰⁾={24°,35°}; F ⁽¹⁾={46°,57°} F⁽²⁾={68°,79°}.  (29)The light waves are s-polarized. The optical material of the substrates110 a and 110 b is as before, Schott N-SF57, having a refractive indexof n_(d)=1.8467 and the optical adhesive is NOA 1315, having arefractive index of n_(d)=1.315. The critical angle is thereforeα_(cr)>45.4°. The FOV of the image that is coupled into, and then from,the device 109, is increased from F⁽⁰⁾={30°, 40°} in the singlesubstrate 64 to F⁽⁰⁾={24°, 40°} in the double substrate element 109. Allthe light waves propagating in the first order and having the combinedFOV of F⁽¹⁾={46°, 60°} have off-axis angles higher than the criticalangle, and therefore, they are totally reflected from the interfaceplane 117 between the substrates. Since the practical output aperture ofeach substrate directly depends on tan α_(sur2), the thickness of thelower substrate 110 b should be slightly increased, in order to equalizethe output apertures of the two substrates. The output aperture ofelement 109 is doubled as compared to that of the single substrate 64 inFIG. 5A and the FOV is increased by 6°. The penalty is that thethickness of the device is doubled and the brightness of the coupled outimage is reduced by 50%. In the event that the left edge of surface 116a is not active, as illustrated above in relation to FIGS. 9A-9C, it ispossible to block this part by slightly shifting the lower substrate 110b. As illustrated in FIG. 11D, the reflecting surfaces 116 a and 116 bare no longer co-linear. The left edge 118 of surface 110 a does notcoincide with the right edge 120 of substrate 110 b, which is slightlyshifted rightward, and hence, the inactive part 122 of surface 110 a ispractically blocked.

Still an alternative embodiment to practically decrease the inputaperture of the optical device is illustrated in FIGS. 12A-12B. Here,the fact that, as illustrated in FIGS. 10A and 10B, the light waveswhich impinge on the left part of the coupling-in surface 65 arereflected only once from surface 65, and hence, propagate inside thesubstrate 64 having the first order off-axis angle of α_(in) ⁽¹⁾, whilethe light waves which impinge on the right part of the coupling-insurface 65 are reflected twice from surface 65, and hence, propagateinside the substrate 64 having the second order off-axis angle of α_(in)⁽²⁾, is exploited. As illustrated in FIG. 12A, an angular sensitivepartially reflecting surface 124 is embedded inside the substrate 64.Surface 124 is parallel to the coupling-in surface 65 and thecoupling-out surface 67, namely, the inclination angle of surface 124 inrelation to the major surfaces of the substrate 64 is:α_(spr)=α_(sur1)=α_(sur2).  (30)For the entire FOV of the image, which is propagating inside thesubstrate 64, surface 124 is substantially transparent for light waveshaving an incident angle ofα_(sp) ⁽⁰⁾=α_(in) ⁽⁰⁾+α_(spr)=α_(in) ⁽¹⁾−α_(spr)  (31)and is substantially, evenly partially, reflective for light waveshaving an incident angle ofα_(sp) ⁽¹⁾=α_(in) ⁽¹⁾+α_(spr)=α_(in) ⁽²⁾−α_(spr).  (32)

In addition, it is assumed that only the left part 125 of thecoupling-in surface 65 is illuminated by the image's light waves. Asillustrated in FIG. 12A, a ray 127 impinges on the left part 125 ofsurface 65, is coupled into the substrate 64 after one reflection fromsurface 65, and hence, propagates inside the substrate 64 having thefirst order off-axis angle of α_(in) ⁽¹⁾. After a few reflections fromthe major surfaces of the substrate 64, the ray 127 impinges on surface124 at point 128 a. Since the ray impinges on the surface from the leftside, it behaves similarly to the rays that impinge on surface 67, andhence, Eq. (16) should be used to calculate to incident angle of ray 127at point 128 a. Hence,α_(sp) ^((128a))=α_(in) ⁽¹⁾−α_(spr).  (33)

As a result, the condition of Eq. (31) is fulfilled and ray 127 passesthrough surface 124 without any significant reflectance. After onereflection from the upper major surface 70, ray 127 impinges again onsurface 124 at point 128 b. Now, the ray impinges on the surface fromthe right side and it behaves similarly to the rays that impinge onsurface 65, and hence, Eq. (15) should be used to calculate to incidentangle of ray 127 at point 128 b. Thus,α_(sp) ^((128b))=α_(in) ⁽¹⁾+α_(spr).  (34)

As a result, the condition of Eq. (32) is fulfilled and ray 127substantially evenly split by surface 124, namely, approximately half ofthe intensity of the light ray passes through surface 124 as ray 129 andcontinues to propagate inside the substrate 124 having the same off-axisangle of α_(in) ⁽¹⁾, while the other half of the intensity of the lightray is reflected from surface 124 as ray 130, and continues to propagateinside the substrate 124 having the off-axis angle ofα_(in) ⁽¹⁾+2·α_(spr)=α_(in) ⁽¹⁾+2·α_(sur1)=α_(in) ⁽²⁾.  (35)

Specifically, ray 130 propagates inside the substrate 64 having thesecond order off-axis angle of α_(in) ⁽²⁾. After one reflection from thelower major surface 72 of the substrate 64, the ray 129 impinges onsurface 124 at the point 128 c. Since the ray again impinges on thesurface from the left side, it behaves similarly to the rays thatimpinge on surface 67, and hence, Eq. (16) should again be used tocalculate to incident angle of ray 129 at point 128 c and, againα_(sp) ^((128c))=α_(in) ⁽¹⁾−α_(spr),  (36)The condition of Eq. (31) is fulfilled, ray 129 passes through surface124 without any significant reflectance and continues to propagateinside the substrate having the first order off-axis angle.Consequently, if the entire left part 125 of surface 65 is illuminatedby all the light waves coupled into the substrate, the substrate 64, asexplained above in relation to FIG. 10A, will be filled by the firstorder of the coupled light waves. After being split by surface 124, partof the light will continue to fill the substrate by the first order,while the part of the light which is reflected by surface 124 will nowfill the second order of the coupled light waves. As a result,substantially the entire aperture of the coupling-out surface 67 will beilluminated by the first and the second orders of the coupled waves andthe output light waves will be coupled-out from substantially the entireactive aperture of surface 67. As a result, while the output apertureremains the entire active aperture of surface 67, the input aperture ofthe substrate is practically reduced by a half. The penalty is that thebrightness of the coupled-out light waves is also reduced by a half.

A similar embodiment for reducing the input aperture by a half isillustrated in FIG. 12B. Here, only the right part of the coupling-insurface 65 is illuminated by the input light waves. As shown, a ray 132impinges on the right part 134 of surface 65, is coupled into thesubstrate 64 after two reflections from surface 65, and hence,propagates inside the substrate 64 having the second order off-axisangle of α_(in) ⁽²⁾. After a few reflections from the major surfaces ofthe substrate 64 the ray 132 impinges on surface 124 at the point 135 a.Since the ray impinges on the surface from the left side it behavessimilarly to the rays that impinges on surface 67, and hence, Eq. (16)should be used to calculate to incident angle of ray 132 at point 135 a.Hence,α_(sp) ^((135a))=α_(in) ⁽²⁾−α_(spr)=α_(in) ⁽¹⁾+α_(spr).  (37)

As a result, the condition of Eq. (32) is fulfilled, and ray 132 issubstantially evenly split by surface 124; approximately half of thelight ray passes through surface 124 as ray 136 and continues topropagate inside the substrate 124 having the same off-axis angle ofα_(in) ⁽²⁾, while the other half of the light ray is reflected fromsurface 124 as ray 137 and continues to propagate inside the substrate124 having the off-axis angle ofα_(in) ⁽²⁾−2·α_(spr)=α_(in) ⁽²⁾−2·α_(sur1)=α_(in) ⁽¹⁾.  (38)

Specifically, ray 137 propagates inside the substrate 64 having thefirst order off-axis angle of α_(in) ⁽¹⁾. After one reflection from thelower major surface 72 of the substrate 64, the ray 137 impinges onsurface 124 at the point 135 b. Since the ray impinges on the surfacefrom the left side, it behaves similarly to the rays that impinge onsurface 67, and hence, Eq. (16) should be used to calculate to incidentangle of ray 127 at point 128 c. Thus,α_(sp) ^((135b))=α_(in) ⁽¹⁾−α_(spr),  (39)the condition of Eq. (29) is fulfilled, ray 137 passes through surface124 without any significant reflectance, and it continues to propagateinside the substrate having the first order off-axis angle.

The practical function of the embodiment illustrated in FIG. 12B issimilar to that illustrated in FIG. 12A. Only half of the input aperture65 is illuminated by the input light waves, while the output light wavesare coupled out from the entire aperture of the coupling-out surface 67.The difference is that while in FIG. 12A only the left part 125 ofsurface 65 is illuminated by the input light waves, in FIG. 12B theright part 134 of surface 65 is used, but the outcome is similar, andthe entire output surface is exploited. Usually, the decision as towhich part of surface 65 to actually use, depends on the variousparameters of the optical system.

The embodiment illustrated in FIGS. 12A-12B, wherein as angularselective reflecting surfaces is embedded inside the substrate 64, canbe exploited for other usages, not necessarily for reducing the inputaperture. An issue that should be considered is the uniformity of theinput light waves that illuminate the input aperture 65. Assuming, forinstance, that the brightness of ray 101 in FIG. 10A is lower than thatof ray 102, as a result of a non-perfect imaging system, this nonsimilarity will hardly be seen by a direct viewing of the input planewave, because of the remoteness between the rays. After being coupledinto the substrate 64, however, this condition changes and the two rays101 and 102 propagate inside the substrate 64 adjacent to each other.Consequently, the two rays that are reflected from surface 67 and arecoupled out from the substrate, have different brightness. Unlike theinput light wave, however, the two rays are now adjacent to each otherand this dissimilarity will be easily seen as a dark line in thecoupled-out image. The same problem occurs if the brightness of ray 106in FIG. 10B is lower than that of ray 105, or vice versa.

FIG. 12C illustrates an embodiment which overcomes this non-uniformityproblem. Here, the same angular sensitive partially reflecting surface124 is embedded inside the substrate 64, but now the entire inputaperture 65 is illuminated by the input light waves. As shown, twodifferent rays, 127 which illuminates the left part 125 close to thecenter of surface 65, and 132 which illuminates the far edge of theright part 134 (and consequently, have lower brightness than ray 127),are propagated inside the substrate 64 having the first and the secondorder off-axis angles, respectively. The two rays coincide at point 138on surface 124 and as explained above in relation to FIGS. 12A and 12B,both of them will be partially reflected by the surface 124 andpartially pass through it. As a result, ray 139, which propagates insidethe substrate having a first order off-axis angle, will be a mixture ofthe part of ray 127 which passes through surface 124, and the part ofray 132 which is reflected by the surface. In addition, ray 140, whichpropagates inside the substrate having a second order off-axis angle,will be a mixture of the part of ray 132 which passes through surface124 and the part of ray 127 which is reflected by the surface. Rays 139and 140 are thus mixtures of the original rays 127 and 132, but unlikethe original rays, the two rays 139 and 140 which are originated fromsurface 124 now have a similar brightness. As a result, assuming thatthe entire aperture of surface 65 is illuminated by the input lightwaves, the uniformity of the light waves that will originate fromsurface 124 will have much better uniform distribution over the outputaperture than previously, and the non-uniformity issue will beconsiderably improved.

Another issue that should be considered is the parallelism between themajor surfaces of the substrate. As explained above in relation to FIGS.4A-4B, the two major surfaces of the substrate 64 should be strictlyparallel to each other, since any deviation between the incident anglesof the trapped light rays on the two major surfaces will cause, at eachreflecting cycle, a drift in the off-axis angle α_(in) ^((i)), and sincethe trapped light rays from the higher order undergo a much smallernumber of reflections from the major surfaces of the substrate thanthose from the lower order, the drift of the low order will be much morenoticeable than that of the high order. There are, however, applicationswherein a very high resolution is required. In addition, the ratiobetween the length and the thickness of the substrate can be high, andhence, the number of reflections from the major surfaces of the lowerorder can be very, and therefore the required parallelism cannot beachieved by conventional fabrication methods.

A possible approach for overcoming the above problem is illustrated inFIG. 12D. An angular sensitive reflecting surface 141, which is parallelto surfaces 65 and 67, is embedded inside the substrate 64, but here thereflecting characteristics of this surface are different than that ofsurface 124 in FIGS. 12A-12C. For the entire FOV of the image whichpropagates inside the substrate 64, surface 141 is substantiallytransparent, as previously, for light waves having an incident angle ofα_(sp) ⁽⁰⁾=α_(in) ⁽⁰⁾+α_(spr)=α_(in) ⁽¹⁾−α_(spr).  (40)For light waves, however, having an incident angle ofα_(sp) ⁽¹⁾=α_(in) ⁽¹⁾+α_(spr)=α_(in) ⁽²⁾α_(spr),  (41)surface 141 is now substantially reflective. As before, surface 141 willbe substantially transparent for the coupled light rays 127 and 132impinging thereon at points 142 and 144, respectively, having a firstorder off-axis angle and impinge on the right side of the surfaces. Forpoint 146 however, where rays 127 and 132 coincide together having afirst order off-axis angle impinging on the left side of surface 141 anda second order off-axis angle impinging on the right side of surface141, respectively, surface 141 will be substantially reflective. As aresult, rays 127 and 132 will be reflected from surface 141 having asecond and a first order off-axis angle, respectively, namely, rays 127and 132 exchange their off-axis angles at the coinciding point 146.Therefore, assuming that surface 141 is located at the center ofsubstrate 64, evenly positioned between surfaces 65 and 67, rays 127 and132 undergo a similar number of reflections from the major surfaces ofthe substrate 64. Assuming that the entire aperture of surface 65 isilluminated by the input light waves, for each input light wave all thecoupled rays will have substantially the same number of reflections fromthe major surfaces of the substrate 64, and the parallelism issue willthus be considerably improved.

The realization of the angular sensitive reflecting surface 124 which isutilized in the embodiments of FIGS. 12A-12C is illustrated hereby withan optical system having the following parameters:α_(sur1)=α_(sur2)=12°; F ⁽⁰⁾={21°,31°}; F ⁽¹⁾={45°,55°} F ⁽²⁾={69°,79°};α_(sp) ⁽⁰⁾{33°,43°}; α_(sp) ⁽¹⁾={57°,67°}.  (42)The light waves are s-polarized. The optical material of the substrate64 is Schott N-SF6 having a refractive index of n_(d)=1.8052, and theoptical adhesive which is adjacent to surface 124 is NTT 6205, having arefractive index of n_(d)=1.71.

FIG. 13 illustrates the graph of the reflection from the reflectivesurface 124 coated with an appropriate angular sensitive dielectriccoating as a function of the incident angle for three differentwavelengths: 450 nm, 550 nm and 650 nm. As shown, the reflection isapproximately 50% for the angular spectrum between 57° and 67°, while itis very low for the incident angles {33°, 43° } of the zero order.

The realization of the angular sensitive reflecting surface 141 utilizedin the embodiment of FIG. 12D, is illustrated hereby with an opticalsystem having same the parameters as those presented above in Eq. 42,where the optical adhesive which is adjacent to surface 141 is NOA 165,having a refractive index of n_(d)=1.52.

FIG. 14 illustrates the graph of the reflection from the reflectivesurface 141 coated with an appropriate angular sensitive dielectriccoating as a function of the incident angle for three differentwavelengths: 450 nm, 550 nm and 650 nm. As shown, the reflection is 100%for the angular spectrum above 57°, while it is practically zero for theincident angles {33°, 43°} of the zero order.

In all the embodiments illustrated in FIGS. 4-11, the coupling-inelement is a slanted reflecting surface. The reason for this is thenecessity to couple the first, as well as the second, order of the lightwaves inside the substrate. For the embodiments illustrated in FIGS.12A-12B, however, where only the first or the second order is,respectively, coupled into the substrate by the coupling-in element,other optical means can be utilized. As illustrated in FIG. 15A, a prism148 is optically attached to the upper major surface 70 of the substrate64. Two light rays 149 and 150 from the same input light wave, impingeon the two edges of the input aperture 152 of the prism 148, where theinclination angle of the light rays inside the prism is α_(in) ⁽¹⁾.While the left ray 149 illuminates the upper major surface 70 just rightto edge 153 of the prism, the right ray 150 passes through surface 70,is totally reflected from the lower surface 72, and then impinges on theupper surface 72 just left to the edge 153. As a result, the two rays149 and 150 are coupled inside the substrate 64, having the first orderoff-axis angle of α_(in) ⁽¹⁾, while propagating inside the substrate 64adjacent to each other. After being partially reflected at points 154and 156 from surface 124, the reflected rays 158 and 160 propagateinside the substrate 20 adjacent to each other having the second orderoff-axis angle of α_(in) ⁽²⁾. Consequently, all the rays of the sameinput light waves covering the input aperture 152, will fill thesubstrate by the first order light waves, and after being partiallyreflected from surface 124, will also fill the substrate by the secondorder light waves. As a result, the output light waves are coupled outfrom the substrate by the entire active aperture of surface 67. Aslightly different embodiment is illustrated in FIG. 15B where thecoupling-in element is a prism 162 which is optically attached to aslanted edge 163 of the substrate. As illustrated, in the embodiments ofFIGS. 15A and 15B, the input aperture is significantly smaller than thatof the embodiments illustrated in FIGS. 4-11. Naturally, realizingmodified embodiments wherein light waves having the second orderoff-axis angles are directly coupled into the substrate utilizingcoupling-in prisms similar to those illustrated in FIGS. 15A and 15B, isalso possible. In that case light waves having the first order off-axisangles will be created inside the substrate in a method similar to thatillustrated in FIG. 12B.

Another issue that should be considered is the uniformity of the lightwaves that are split by surface 124 in the embodiments of FIGS. 12A-12C.As illustrated, the trapped) rays having the first order off-axis angleof α_(in) ⁽¹⁾ are partially reflected only once from the left side ofsurface 124. As illustrated in FIG. 16A, there are rays, however, whichare partially reflected twice from surface 124. As shown, ray 164 isfirst partially reflected from surface 124 at point 165, located inproximity to the intersection between surface 124 and the upper majorsurface 70. The part of ray 164 which passes through surface 124 atpoint 165 is reflected from the lower major surface 72, passes throughsurface 124, is reflected from the upper surface 70 and then ispartially reflected again from surface 124 at point 166. Since thebrightness of this part of the ray has been already reduced by a half,while splitting at point 165, the brightness of the split rays frompoint 166 will be approximately 25% of that of the original ray 164,namely, ray 164 has been split into three different rays: ray 164 awhich is reflected from surface 124 at point 165 and has about a half ofthe brightness of the original ray 164, and rays 164 b and 164 c, whichpass through surface 164 at point 165 and then pass again, or arereflected, respectively, by surface 164 at point 166, which rays haveabout a quarter of the brightness of the original ray 164. As a result,there are rays in the image waves which are less bright than the others,and these variations might be seen as dark stripes in the coupled-outimage. This phenomenon is negligible for the light waves having thehigher off-axis angles in the FOV, but it is, however, more significantfor the light waves having the lower off-axis angles.

In order to solve the unevenness problem of the image which is coupledout from the substrate, it is important to understand the differencebetween this problem and an unevenness problem of a conventional displaysource which emits a real image from the display plane. Generally, theunevenness of an image, which is projected from a conventional displaysource, is caused by the non-uniformity of the display itself, e.g.,different pixels of the display emit light waves having differentintensities. As a result, the only way to solve the unevenness problemis to directly manage the pixels of the display. The cause for theunevenness of the image illustrated hereinabove in relation to FIG. 16A,however, is completely different. Here, the unevenness is caused by anon-uniformity of the different rays of a single light wave, which isassociated with a single pixel in the image, meaning that different raysbelonging to the same plane light wave, and consequently having the samedirection, have different intensities. Therefore, the unevenness of thisplane wave can be solved if the various rays of this uneven wave will bemixed together. Hence, a proper mixing arrangement should beadvantageously be added to the substrate 64, in order to improve theuniformity of the plane waves, which are trapped inside the substrate bytotal internal reflection.

As illustrated in FIG. 16B, this unevenness problem may be solved byattaching a flat transparent plate 167 to one of the major surfaces 72of the substrate 64, wherein a beam-splitting arrangement is applied tothe interface plane 168 between the substrate 64 and the transparentplate 167. As illustrated, two light rays, 164 and 169, having differentintensities intersect each other at point 170 located at the interfaceplane 168. Ray 164, which is illustrated above in FIG. 16A, has alreadybeen partially reflected by surface 124, and hence, has a lowerbrightness then the original ray. The other ray 169, which passesthrough the interface plane at point 171 and is reflected by the lowersurface 172 of the plate 167, did not yet pass through surface 124, andhence, it has a higher intensity. As a result of the beam-splittingarrangement which is applied there, each one of the two intersectingrays is partially reflected and partially passes through the interfaceplane. Consequently, the two rays interchange energies betweenthemselves, and the emerging ray 164 d from the intersection point 170has an intensity which is closer to the average intensity of the twoincident rays 164 and 169. As a result, the intensity of ray 164 d,which is partially reflected by surface 124 at point 166, is higher thanpreviously and the non-uniformity problem is relaxed. (There are moreintersections and splitting of rays 164 and 169 in FIG. 16B but tosimplify the figure, only the intersection at point 170 and the emergingof ray 164 d from there is plotted). In addition to the mixing of rays164 and 169 at point 170, rays 164 b and 164 c which emerged from point166 are mixed again with other rays (not shown) at points 174 and 175,respectively, on the interface plane 168, and their intensities becomeeven closer to the average intensity of the coupled-out image wave.

The most efficient beam-splitting arrangement is to apply a partiallyreflecting coating to the interface plane, wherein half of the incominglight wave is transmitted and half is reflected from the surface. Inthat case, the intensities of the emerging ray 164 d are substantiallythe average intensity of the two incident rays 164 and 169, and themixing between the rays is optimal. The main drawback of the coatingmethod, however, is that in order to avoid aberrations and smearing ofthe image, the direction of the trapped rays inside the substrate shouldbe strictly retained. Therefore, a high degree of parallelism should bemaintained for the three reflecting surfaces: the upper surface 70 ofthe substrate 64, the lower surface 172 of the plate 167 and theinterface plane 168. As a result, the external surfaces of the substrate64 and the plate 167 should have high parallelism and very good opticalquality before attaching them together. Applying an optical coating toone of these external surfaces, however, will require a coating processwhich usually deforms the surfaces of the coated plate, especially ifthis plate is particularly thin. Another problem is that the light rayswhich are reflected from surface 67 intersect with the interface plane168 before being coupled out from the substrate 64. As a result, asimple reflecting coating cannot easily be applied to the interfaceplane 168, since this plane should also be transparent to thelight-waves that exit the substrate 64, as well as transparent to thelight wave from the external scene for see-through applications. Thus,the light-waves should pass through plane 168 without substantialreflections at small incident angles and should be partially reflectedat higher incident angles. This requirement complicates the coatingprocedure and increases the probability that the coated plate will bedeformed during the coating process. Consequently, since even a minordeformation will deteriorate the performance of the imaging system, analternative mixing arrangement should be applied.

An alternative embodiment is illustrated in FIG. 16C. Here, thesubstrate 64 and the plate 167 are optically cemented using an opticaladhesive 176 having a refractive index, which is substantially differentthan the refractive index of the light transmitting substrate 64 and theflat plate 167. As a result of the differences between the refractiveindices and the oblique incident angles of the trapped rays, as comparedto the interface plane 168, the Fresnel reflections from plane 168 willbe significant and the light waves which are coupled inside thesubstrate, will be partially reflected from the interface plane.Practically, the incident rays are reflected twice from the interfaceplane 168, once from the interface plane between the substrate 64 andthe adhesive 176, and the second time from the interface plane betweenthe optical adhesive 176 and the transparent plate 167. As illustrated,three different rays 164, 169 and 178 are trapped inside the substrate.The two rays 169 and 178 intersect each other at point 171 which islocated at the interface plane 168. As a result of the Fresnelreflections, each one of the two intersecting rays is partiallyreflected and partially passes through the interface plane.Consequently, the two rays interchange energies between themselves andthe emerging rays 179 and 180 from the intersection point 171 haveintensities which are closer to the average intensity of the twoincident rays 169 and 178. Similarly, the two rays 164 and 179 intersecteach other at point 170, interchange energies between themselves and theemerging rays 181 and 182 from the intersection point 170 haveintensities which are closer to the average intensity of the twoincident rays 164 and 179. Therefore, the three rays 164, 179 and 178,interchange energies during this process and their intensities are nowcloser to the average intensity. Rays 164 and 178 do not interchangeenergies directly, but indirectly through the two separate interactionswith ray 179, at points 170 and 171.

The optimal mixing will be achieved if the Fresnel reflections from theinterface plane 168 are close to 50%. Since, however, Fresnelreflections are very sensitive to the incident angle, it is impossibleto find an optical adhesive having a refractive index that yieldsFresnel reflection of 50% for the entire FOV of the coupled image, andsince the trapped rays intersect not only once, but rather a few timeswith the interface plane, it is possible to find a mixing arrangementthat will be acceptable even for Fresnel reflections which are verydifferent than the optimal value of 50%. The realization of the raymixing interface plane 167 which is utilized in the embodiments of FIGS.16B-16C is illustrated herein with an optical system having sameparameters as given above in Eq. 42, where the optical adhesive which isused to cement the substrate 64 with the flat plate 167, is NTT-E3341having a refractive index of n_(d)=1.43.

FIG. 17 illustrates a graph of the reflection from the interface plane167 as a function of the incident angle for the wavelength 550 nm (theother wavelengths in the photopic region have similar curves) for theentire first order FOV F⁽¹⁾={45°, 55°}. As shown, the reflection is 100%for the angular spectrum above 53° as a result of total internalreflection, and hence, no mixing effect is achieved for these angles.For the entire second order FOV F⁽²⁾={69°, 79°}, all the light waves aretotally internally reflected from the interface plane 168 and no mixingeffect is achieved for the entire order. As has been explained above,however, the non-uniformity problem is substantially negligible for therays having these angles. For the other spectral range of α_(in)⁽¹⁾<52°, the reflection is between 20% and 80%, and a good mixing effectcan be achieved. In addition, the device illustrated here is not limitedto utilization of a single flat plate. Two or more flat plates, havingvarious thicknesses and refractive indices, can be optically attached toone or both of the major surfaces using various optical adhesives. Inany case, the exact parameters of the transparent plates and theadhesives can be used according to the various requirements of thesystems.

In the embodiment 109 illustrated in FIGS. 11A-11D, it was assumed thatthe beamsplitter 114 a evenly splits each input ray into two rays, whichhave substantially the same brightness and are coupled inside substrates110 a and 110 b, by total internal reflection. As a result, thebeamsplitter 114 a is not sensitive to the incidence angle of the inputlight wave, and in addition, the output brightness is reduced by about50%. FIGS. 18A-18C illustrate a modified version of device 109, whereinthe input beamsplitter 183 is sensitive to the incident angle of theinput light waves and, as a result the efficiency of the optical system,is significantly improved and the brightness of the coupled-out image issubstantially retained similar to that of the input image. To achievethis improvement, the fact that the light waves which are coupled outfrom the substrate do not have to illuminate the entire active area ofthe coupling-out surface, as was done in the embodiments of FIGS.11A-11D, was utilized.

As illustrated in FIG. 19, showing the rays that should impinge onsurface 79 in order to illuminate the EMB 197, the two marginal and thecentral light waves of the image are coupled out from the substrate andre-directed into the viewer's eye 24. As shown, the light waves 107R,107M, and 107L, having the zero order off-axis angles α_(in) ⁽⁰⁾(max),α_(in) ⁽⁰⁾(mid) and α_(in) ⁽⁰⁾(min), illuminate only the parts 67R, 67Mand 67L of the coupling-out reflecting surface 67, respectively, and arereflected by surface 79 into to EMB 197. As a result, a method can befound where the coupled-in light waves are split in such a way that theywill illuminate only the required respective part of surface 67, and theoriginal brightness will be preserved. To achieve this, the angularrange of the light waves F_(sur1) ⁽⁰⁾≡{α_(min), α_(max)}, which impingeon the input surface 183 (FIG. 18A), is divided into three substantiallyequal segments: F_(low) ⁽⁰⁾≡{α_(min), α_(m1)}, F_(mid) ⁽⁰⁾≡{α_(m1),α_(m2)} and F_(max) ⁽⁰⁾≡{α_(m2), α_(max)}. The aim of the embodiment isthat the light waves having the higher incident angles in the FOV ofF_(max) ⁽⁰⁾≡{α_(m2), α_(max)} will be coupled out from the uppersubstrate 110 a by the both parts of the coupling-out element 190 a and190 b; the light waves having the lower incident angles in the FOV ofF_(min) ⁽⁰⁾≡{α_(min), α_(m1)} will be coupled out from the lowersubstrate 110 b by the both parts of the coupling-out element 190 c and190 d, and the light waves in the FOV of F_(mid) ⁽⁰⁾≡{α_(m1), α_(m1)}will be coupled out from the upper substrate 110 a by the lowercoupling-out element 190 b and from the lower substrate 110 b by theupper coupling-out element 190 c.

In order to achieve this, surface 183 should substantially reflect allthe light waves in F_(max) ⁽⁰⁾ such that they will be coupled into theupper substrate 110 a and substantially transmit all the light waves inF_(min) ⁽⁰⁾, such that they will be coupled by the reflecting surface114 into the lower substrate 110 b. In addition, part of the light wavesin F_(mid) ⁽⁰⁾ should be reflected by surface 183 in such a way thatthey will be trapped inside the upper substrate 110 a, but will becoupled out only by the lower part of the coupling-out element 190 b andpart of the light waves in F_(mid) ⁽⁰⁾ should be pass through surface183 in such a way that they will be trapped inside the lower substrate110 b but will be coupled out only by the upper part of the coupling-outelement 190 c. As illustrated in FIGS. 4A and 4B, the light waves whichpropagate inside the substrate having the first order off-axis anglesare coupled out from the substrate by the upper part of the coupling-outelement 67, while the light waves propagating inside the substratehaving the second order off-axis angles are coupled out from thesubstrate by the lower part of the coupling-out element 67. Therefore,in order to achieve the coupling-in requirements of the light waves inF_(mid) ⁽⁰⁾, it is necessary for the light waves in this FOV to becoupled inside the upper substrate 110 a having the second orderoff-axis angles, and hence, will be coupled out by the lower part 190 b,and in addition, will be coupled inside the lower substrate 110 b havingthe first order off-axis angles, and hence, will be coupled out by theupper part 190 c.

Consequently, the angular sensitive reflecting surface 183 shouldfulfill the following three characteristics for the entire photopicrange:

-   -   a. substantially total reflective for the angular range of        {α_(m2), α_(max)};    -   b. substantially transparent for the angular range of {α_(min),        α_(m1)}; and    -   c. substantially total reflective for the angular range of        {α_(m1), α_(m2)} at the upper part 183 a (FIG. 18C) of surface        183 and substantially transparent for the angular range of        {α_(m1), α_(m2)} at the lower part 183 b (FIG. 18C) of surface        183.

It is possible to achieve these requirements by applying angularsensitive dielectric coatings on surfaces 183 a and 183, but therealization process of these coatings can be fairly complicated. Asimpler method is to cement surfaces 183 a and 183 b to the inert part177 of device 109 using optical adhesives having proper refractiveindices that yield critical angles of α_(m1) and, α_(m2) at surfaces 183a and 183 b, respectively. The high transparency for angles lower thanthe respective critical angles can be achieved using proper AR coatings

FIG. 18A illustrates two rays 184 a and 184 b from the same plane inputwave having incident angles of α_(si) ⁽⁰⁾<α_(m1) which impinge on thelower and the upper parts of surface 183, respectively. As a result ofcondition (b) described hereinabove, the rays pass through surface 183and are coupled into the lower substrate 110 b by the reflective surface114 having the first and the second order off-axis angles, respectively.Consequently, the rays are coupled-out from the substrate by thereflective surfaces 190 c and 190 d, respectively. FIG. 18B illustratestwo rays 185 a and 185 b from the same plane input wave having incidentangles of α_(si) ⁽⁰⁾>α_(m2) which impinge on the lower and the upperparts of surface 183, respectively. As a result of condition (a)described hereinabove, the rays are reflected from surface 183 and arecoupled into the upper substrate 110 a having the first and the secondorder off-axis angles, respectively. Consequently, the rays arecoupled-out from the substrate by the reflective surfaces 190 a and 190b respectively. FIG. 18C illustrates two rays 186 a and 186 b from thesame plane input wave having incident angles of α_(m1)<α_(si)⁽⁰⁾<α_(m2), which impinge on the surfaces 183 b and 183 a, respectively.As a result of condition (c) described hereinabove, ray 186 b isreflected from surface 183 a and is coupled into the upper substrate 110a having the second order off-axis angle. Consequently, the ray iscoupled-out from the substrate by the lower reflective surface 190 b. Inaddition, ray 186 a passes through surface 183 b and is coupled into thelower substrate 110 b by the reflective surface 114 having the firstorder off-axis angle. Consequently, the ray is coupled-out from thesubstrate by the upper reflective surfaces 190 c, as required.

Usually, it will be difficult to cement surface 183 to the inert part177 such that the two parts 183 a and 183 b will be cemented to part 177by two different adhesives, without any cross-talk between the parts. Asillustrated in FIG. 18C, a possible way for overcoming this problem isby fabricating substrate 110 a of two parallel slices 110 aa and 110 ab,attached together at the interface plane 189. Three critical issuesshould be considered during the fabrication process of the uppersubstrate 110 a as a combination of 110 aa and 110 ab. Firstly, in orderto avoid the trapping of the second order light waves in the upper slice110 aa by total internal reflection from the interface plane 189, it isessential that the optical adhesive used to optically attach the slices110 aa and 110 ab will have a refractive index close to that of theslices. In addition, in order to prevent distortion of the coupled-outimage, the coupling in surfaces 183 a and 183 b and the coupling-outsurfaces 190 a and 190 b should be strictly co-linear, respectively.Furthermore, since it will be difficult to completely prevent residualFresnel reflections of the trapped light waves, especially those havingthe second order off-axis angles, the interface plane 189 should beparallel to the major surfaces 111 a and 112 a of substrate 110 a.

An alternative embodiment to realize the required angular-sensitivebeamsplitter is illustrated in FIGS. 20A-20C. As shown, the overalloptical device 199 is constructed of four different substrates 191 a,191 b, 191 c and 191 d, which are optically cemented together definingthree interface planes, 193 a, 193 b and 193 c, respectively. Anotherdifference from the embodiment of FIGS. 18A-18C is that here thebeamsplitters 183 a and 183 b are interchanged, e.g., surfaces 183 a and183 b are cemented to the inert part 177 of element 199 using opticaladhesives having proper refractive indices that now yield criticalangles of α_(m1) and, α_(m2) at surfaces 183 b and 183 a, respectively.

FIG. 20A illustrates two rays 184 a and 184 b from the same plane inputwave having incident angles of α_(si) ⁽⁰⁾<α_(m1), which impinge onsurface 183 b and 183 a, respectively. As previously, the rays passthrough the surfaces and are coupled into the substrates 191 d and 191 cby the reflective surfaces 195 b and 195 a, respectively. Although therays plotted in the figure have only the first order off-axis angles, itis clear that the input light waves illuminate the entire areas ofsurfaces 195 a and 195 b, and hence, they fill the entire first andsecond off-axis angles and as a result illuminate the entire activeareas of surfaces 190 c and 190 d which couple them out of thesubstrates.

FIG. 20B illustrates two rays 185 a and 185 b from the same plane inputwave having incident angles of α_(si) ⁽⁰⁾>α_(m2), which impinge onsurface 183 b and 183 a, respectively. As previously, the rays arereflected from the surfaces and are coupled into the substrates 191 band 191 a, respectively. As described above, the input light wavesilluminate the entire areas of surfaces 183 a and 183 b, and hence, theyfill the entire first and second off-axis angles and as a resultilluminate the entire active areas of surfaces 190 a and 190 b, whichcouple them out of the substrates.

FIG. 20C illustrates two rays 186 a and 186 b from the same plane inputwave having incident angles of α_(m1)<α_(si) ⁽⁰⁾<α_(m2), which impingeon the surfaces 183 b and 183 a, respectively. Since the beam-splittingmechanism was interchanged between surfaces 183 a and 183 b, ray 186 ais now reflected from surface 183 b, and is coupled into substrate 191 band coupled out by the reflective surface 190 b. In addition, ray 186 bnow passes through surface 183 a and is coupled into substrate 191 c bythe reflective surface 195 a, and consequently, is coupled-out from thesubstrate by the reflective surface 190 c as required. Since each one ofthe four substrates 191 i (i=a, b, c, d) functions independently, thereare no longer any constraints on the co-linearity of each adjacentcoupling-in and coupling-out surfaces as there were according to theembodiments of FIGS. 18A-18C. The only constraint is that for eachseparate substrate 191 i, the major surfaces and the coupling-in and thecoupling-out surfaces should be parallel to each other, respectively.Moreover, each separate substrate can have a different thickness and adifferent inclination angle according to the requirements of the opticalsystem.

The implementation of the angular sensitive reflecting surfaces 183 sand 183 b utilized in the embodiments of FIGS. 18A-18C and 20A-20C isillustrated herein with an optical system having the followingparameters for substrate 110 a of FIGS. 18A-18C and substrates 191 a and191 b of FIGS. 20A-20C:α_(sur1)=α_(sur2)=9°; F ⁽⁰⁾={36°,46°}; F ⁽¹⁾={54°,64°} F ⁽²⁾={72°,82°};α_(sp) ⁽⁰⁾={45°,55°}; α_(sp) ⁽¹⁾={63°,73°},  (43)

and the following parameters for substrate 110 b of FIGS. 18A-18C andsubstrates 191 c and 191 d of FIGS. 20A-20C:α_(sur1)=α_(sur2)=10°; F ⁽⁰⁾={30°,40°}; F ⁽¹⁾={50°,60°} F ⁽²⁾={70°,80°};α_(sp) ⁽⁰⁾={40°,50°}; α_(sp) ⁽¹⁾={60°,70°}.  (44)The light waves are s-polarized. The optical material of the substrate64 is Schott N-SF57 having a refractive index of n_(d)=1.846, and theoptical adhesives which are adjacent to surfaces 183 a and 183 b inFIGS. 18A-18C (or surfaces 183 b and 183 a in FIGS. 20A-20C) areNTT-E3337 and NOA 1315, having refractive indices of n_(d)=1.315 andn_(d)=1.42, respectively. The overall FOV of the coupled-in image isF⁽⁰⁾={30°, 46°} (which is practically a FOV of 30° in the air) and theangular range of F_(sur1) ⁽⁰⁾≡{39°, 55°} is divided into threesubstantially equal segments: F_(low) ⁽⁰⁾≡{39°, 45°}, F_(mid) ⁽⁰⁾≡{45°,50°} and F_(max) ⁽⁰⁾≡{50°, 55°}.

FIG. 21A illustrates the graph of the reflection from the reflectivesurface 183 a in FIG. 18C (or surface 183 b in FIG. 20C) coated with anappropriate AR dielectric coating as a function of the incident anglefor three different wavelengths: 450 nm, 550 nm and 650 nm. As shown,the reflection is 100%, due to total internal reflection, for angularspectrum is above 45.6°, while it is very low for the incident angles of{39°, 44.5°}. FIG. 21B illustrates the graph of the reflection from thereflective surface 183 b in FIG. 18C (or surface 183 a in FIG. 20C)coated with an appropriate AR dielectric coating as a function of theincident angle for three different wavelengths: 450 nm, 550 nm and 650nm. As shown, the reflection is 100%, due to total internal reflection,for angular spectrum above 50.7°, while it is very low for the incidentangles of {39°, 50°}.

FIG. 22 illustrates the two marginal and the central light waves of theimage which are coupled out from the substrate and re-directed into theviewer's eye 24. As shown, the light waves 185, 186, and 184, having thezero order off-axis angles of α_(in) ⁽⁰⁾(max), α_(in) ⁽⁰⁾(mid) andα_(in) ⁽⁰⁾(min), are illuminating each only the reflection surfaces 190a-190 b, 190 b-190 c and 190 c-190 d, respectively, and are reflected bysurface 79 into to EMB 197. The extent of the EMB 197 is set by the twomarginal rays 185R and 184L, which are reflected form the two edges ofthe overall coupling-out aperture of element 199, and is not influencedat all by the rays 185R and 184L which “moved” to the center of thecoupling-out aperture as a result of the new arrangement. Consequently,the EMB 197 of the embodiment which is illustrated in FIGS. 18A-18C and20A-20C has the same large aperture as the EMB of the embodiment whichis illustrated in FIGS. 11A-11C, while the output brightness is doubled.

FIGS. 20A, 20B and 20C illustrate outlines of embodiments comprising twopairs of substrates, wherein the output aperture is increased by afactor of two without reducing the brightness of the projected image.There are systems, however, having a wide FOV and an input apertureremotely located from the EMB, which significantly increases therequired input aperture of the main substrate. In these cases,increasing the aperture by a factor of two in not enough and a higherincreasing factor is required. To achieve this goal, theabove-illustrated increasing method can be generalized to increasingfactors of n>2. Assuming that it is required to increase the aperture ofthe image by a factor of n, n pairs of transparent substrates should beattached together, wherein for each pair the coupling-in, as well as thecoupling-out, surfaces should be adjacently located in the same manneras, for example, surfaces 183 a and 183 b, and 190 a and 190 b (FIG.20A), respectively. In addition, all the coupling-out surfaces should beadjacently located as surfaces 190 i in embodiment 199. The angularrange of the light waves which impinge on the input surface of the upperpair F_(sur1)≡{α_(min), α_(max)} is divided now into 2n−1 substantiallyequal segments, by setting 2n−2 equally separated angles α_(j). That is,F₁≡{α_(min), α₁}, F₂≡{α₁, α₂} . . . F_(j)≡{α_(j−1), α_(j)} andF_(2n-1)≡{α_(2n-2), α_(max)}. Assuming that the substrates are denotedas S_(j), where j is the running index from bottom (j=1) to top (j=2n),then the coupling-in elements of substrates S₁ and S₂ from the lowerpair are regular reflecting surfaces. All the other 2n−2 coupling-inelements are angular sensitive partially reflecting surfaces fulfilling,for each substrate S_(j) (j>2), the following conditions for the entirephotopic range:

-   -   a. substantially totally reflective for the angular range of        α_(si) ⁽⁰⁾>α_(j−2), and    -   b. substantially transparent for the angular range of α_(si)        ⁽⁰⁾<α_(j−2).

That is to say, the coupling-in element of substrate S_(j) shouldreflect all the impinging light waves having incident angles higher thanthe limit angle of α_(j−2), to couple these light waves inside substrateS_(j), and to substantially transmit all the other light waves towardthe input aperture of substrate S_(j−2). As explained above, thesimplest way to achieve these requirements is to cement each respectivecoupling-in surface to the adjacent inert part of the embodiment, usingoptical adhesives having proper refractive indices that yield criticalangles of α_(j−2). As previously described, the high transparency forincident angles lower than the respective critical angles, can beachieved using proper AR coatings.

The above illustrated embodiments, comprising n pairs of transparentsubstrates, will have the following characteristics:

-   -   a. aside from the bottom and the top substrates, the light waves        which are coupled inside each substrate S_(j) (j=2 . . . 2n−1)        are those in the angular range of {α_(j−2), α_(j)} (α_(min) and        α_(max) are denoted here as α₀ and α_(2n-1) respectively). The        light waves coupled inside substrates S₁ and S_(2n) are those in        the angular ranges of {α₀, α₁} and {α_(2n-2), α_(2n-1)},        respectively.    -   b. each light wave (inside the angular range of the light waves        which impinge on the input surface of the upper pair        F_(sur1)≡{α_(min), α_(max)}) having an incident angle of        α_(j−1)<α_(s)<α_(j) (j=1 . . . 2n), is coupled inside two        adjacent substrates—S_(j) and S_(j+1) and is consequently        coupled out from the embodiment by the respective coupling-out        element 190 _(j) and 190 _(j+1). Therefore, each light wave        which is coupled inside the embodiment by total internal        reflection, is coupled out by 1/n part of the overall        coupling-out element. By a proper design, however, substantially        all the coupled light waves will cover the designated EMB of the        system.

In all the embodiments illustrated in FIGS. 11-20, one of the outcomesof expanding the output aperture is that the thickness of the opticalmodule is also expanded, accordingly. There are applications however,where it is required to have a large output aperture while still keepingthe substrate as thin as possible. FIG. 23A illustrates an embodimentwherein the output aperture is expanded without increasing thesubstrate's thickness. As shown, an angular sensitive partiallyreflecting surface 198 is embedded inside the substrate 200. Surface 198is parallel to the coupling-in surface 65 and the coupling-out surface67. The inclination angle of surface 198 in relation to the majorsurfaces of the substrate 200 is:α_(prs)=α_(sur1)=α_(sur2)  (45)For the entire FOV of the image propagating inside the substrate 200,surface 198 is substantially evenly partially reflective, that is, itevenly reflects and transmits the coupled-in light waves having anincident angle ofα_(sp) ⁽⁰⁾=α_(in(0))+α_(spr)=α_(in) ⁽¹⁾−α_(spr)  (46)and is totally reflective for light waves having an incident angle ofα_(sp) ⁽¹⁾=α_(in) ⁽¹⁾+α_(spr)=α_(in) ⁽²⁾−α_(spr).  (47)

In addition, the surface is substantially transparent for the lightwaves which are coupled-out from the substrate and re-directed into theviewer's eye, as well as for the light waves from the external scene.

As illustrated in FIG. 23A, a ray 202 is coupled into the substrate 200after one reflection from surface 65, and hence, propagated inside thesubstrate 200 having the first order off-axis angle of α_(in) ⁽¹⁾. Aftera few reflections from the major surfaces of the substrate 200, the ray202 impinges on surface 198 at the point 206 a. Since the ray impingeson the surface from the left side, it behaves similarly to the rays thatimpinge on surface 67, and hence, Eq. (16) should be exploited tocalculate to incident angle of ray 202 at point 206 a, namely,α_(sp) ^((206a))=α_(in) ⁽¹⁾−α_(spr).  (48)

As a result, the condition of Eq. (46) is fulfilled, and ray 202 issubstantially evenly split by surface 198, namely, approximately half ofthe intensity of the light ray 202 is reflected from surface 198 as ray202 a having the off-axis angle of α_(in) ⁽⁰⁾, and hence, is coupled outfrom the substrate 200 through the lower surface 72. The other half ofthe intensity of the light ray 202 passes through surface 198 as ray 202b and continue to propagate inside the substrate 200 having the sameoff-axis angle of α_(in) ⁽¹⁾. After one reflection from the upper majorsurface 70, ray 202 b impinges again on surface 198 at point 206 b. Now,the ray impinges on the surface from the right side, and it behavessimilarly to the ray that impinges on surface 65, and hence, Eq. (15)should be used to calculate to incident angle of ray 202 b at point 206b, so thatα_(sp) ^((206b))=α_(in) ⁽¹⁾+α_(spr).  (49)

As a result, the condition of Eq. (47) is fulfilled and ray 202 b istotally reflected form surface 198, and continues to propagate insidethe substrate 200 having the off-axis angle ofα_(in) ⁽¹⁾+2·α_(spr)=α_(in) ⁽¹⁾+2·α_(sur1)=α_(in) ⁽²⁾.  (50)

Specifically, ray 202 b propagates inside the substrate 200 having thesecond order off-axis angle of α_(in) ⁽²⁾. After two reflections fromthe coupling-out surface 67, ray 202 b is coupled out from substrate 200having the same off-axis angle α_(in) ⁽⁰⁾ as ray 202 a.

As also illustrated in FIG. 23A, another ray 204 is coupled into thesubstrate 200 after two reflections from surface 65, and hence,propagates inside the substrate having the second order off-axis angleof α_(in) ⁽²⁾. After a few reflections from the major surfaces of thesubstrate 64, the ray 204 impinges on surface 198 at point 207 a. Sincethe ray impinges on the surface from the left side and behaves similarlyto the rays that impinge on surface 67, Eq. (16) should hence be used tocalculate the incident angle of ray 204 at point 207 a. Hence,α_(sp) ^((207a))=α_(in) ⁽²⁾−α_(spr)=α_(in) ⁽¹⁾+α_(spr).  (51)As a result, the condition of Eq. (47) is fulfilled and ray 204 istotally reflected from surface 198 and continues to propagate inside thesubstrate 200 having the off-axis angle ofα_(in) ⁽²⁾−2·α_(spr)=α_(in) ⁽²⁾−2·α_(sur1)=α_(in) ⁽¹⁾.  (52)

Specifically, ray 204 propagates inside the substrate 200 having thefirst order off-axis angle of α_(in) ⁽¹⁾. After one reflection from thelower major surface 72 of the substrate 200, the ray 204 impinges againon surface 198 at the point 207 b. Similarly to the behavior of ray 202at point 206 a, ray 204 is substantially evenly split by surface 198.Approximately half of the intensity of the light ray 204 is reflectedfrom surface 198 as ray 204 a having the off-axis angle of α_(in) ⁽⁰⁾,and hence, is coupled out from the substrate 200 through the lowersurface 70. The other half of the intensity of the light ray 204 passesthrough surface 198 as ray 204 b and continues to propagate inside thesubstrate 200 having the same off-axis angle of α_(in) ⁽¹⁾. After onereflection from the coupling-out surface 67, ray 204 b is coupled outfrom substrate 200 having the same off-axis angle α_(in) ⁽⁰⁾ as rays 202a, 202 b and 204 a. As a result, the output aperture of substrate 200 isthe combination of surfaces 198 and 67. Consequently, the practicalactive area of the output aperture of substrate 200 has been doubled ascompared to that of substrate 64, which is illustrated in FIG. 4, whilethe thickness of the substrate remains the same. On the other hand, thebrightness of light waves coupled out from substrate 200 has beenreduced by 50% as compared to that of substrate 64.

The expanding embodiment illustrated in FIG. 23A is not limited to onesubstrate or only one partially reflecting surface. Optical systemswhich are composed of a few different substrates, or a few differentpartially reflecting surfaces which are embedded inside a singlesubstrate, are also feasible. FIG. 23B illustrates an optical system 208wherein two different substrates 210 a and 210 b are attached together.Two partially reflecting surfaces 212 a and 212 b, having the sameoptical characteristics as surface 198 in FIG. 23A, are embedded insidesubstrates 210 a and 210 b, respectively. An input ray 214 is split bythe beam-splitting surface 216 into two parts: a ray 214 a which iscoupled by surface 216 into substrate 210 a, and ray 214 b which passesthrough surfaces 216 and is coupled by surface 218 into substrate 210 b.The coupled rays 214 a and 214 b are split by surfaces 212 a and 212 brespectively. The rays 214 aa and 214 ba are reflected by these surfacesand coupled out from the substrate, while rays 214 ab and 214 bb passthrough theses surfaces and are coupled out from the substrate by thereflecting surfaces 220 a and 220 b, respectively. As a result, theoutput aperture of the system 208 is composed of four surfaces: 212 a,212 b, 220 a and 220 b, and the active area of this aperture is expandedaccordingly. As shown, in embodiment 208, the coupling-out surfaces 212b and 220 b of the lower substrate 210 b partially can block, ifrequired, the non-active parts of surfaces 212 a and 220 a,respectively.

In the embodiments illustrated in FIGS. 23A and 23B, it was assumed thatthe partially reflecting surfaces which are embedded in the substratesevenly split the intensities of the impinging light waves, namely, thereflectance (and hence, the transmittance) of the surface is 50% for theentire angular spectrum of the coupled image. It should be notedhowever, that due to the same arguments which were considered inrelation to FIGS. 19 and 22, that the light waves having off-axis anglesin the upper part of the angular spectrum of the image, are mostlycoupled out into the EMB by the partially reflective surface 198, whilethe light waves having off-axis angles in the lower part of the angularspectrum of the image, are mostly coupled out into the EMB by thereflective surface 67. As a result, it will be advantageous to provide apartially reflective coating on the partially reflecting surface thatwill have a reflectance higher and lower than 50% for the upper andlower regions of the angular spectrum, respectively. In that case, sincethe brightness of the light waves in the upper and lower regions dependson the reflectance and transmittance of the partially reflecting surface198, respectively, it will be higher than 50% for these regions. On theother hand, for the light waves in the central region of the angularspectrum, which are evenly coupled out into the EMB by the partiallyreflecting surface 198 and the reflecting surface 67, the reflectanceand accordingly, the brightness, will be around 50%, which is slightlylower than the brightness at the edges of the image. For most of theback and front illuminated displays, such as LCD and LCOS, however, theillumination, and hence, the brightness of the display sources, areusually stronger at the center of the display. As a result, thenon-uniform reflectance curve of the partially reflecting surface cancompensate for the non-uniform illumination and in addition the overallbrightness of the coupled-out image is improved.

An alternative embodiment 255, wherein the output aperture is expandedwithout increasing the substrate's thickness and without the necessityto resort to a special partially reflecting coating as required forsurface 198, is illustrated in FIG. 23C. As shown, a reflecting surface256 is embedded inside the substrate 258. Surface 256 has the samereflecting characteristics as surface 67 and is parallel to thecoupling-in 65 and the coupling-out 67 surfaces. The inclination angleof surface 256 in relation to the major surfaces of the substrate 258is:α_(sur3)=α_(sur1)=α_(sur2)  (53)

As shown in FIG. 23C, a ray 260 is coupled into the substrate 258 afterone reflection from surface 65, and hence, propagates inside thesubstrate 258 having the first order off-axis angle of α_(in) ⁽¹⁾. Aftera few reflections from the major surfaces of the substrate 258 the ray260 impinges on surface 256. Since the ray impinges on the surface fromthe right side, it behaves similarly to the rays that impinges onsurface 67, and hence, it is coupled out from the substrate 258 havingan off-axis angle α_(in) ⁽⁰⁾ and is then reflected (or partiallyreflected in see-through applications) into the viewer's eye similarlyto what is illustrated in FIGS. 5A-5C. The reflected ray is, however,not propagated here undisturbed into the viewer's eye, as in theembodiments illustrated in FIGS. 5A-5C. Instead, the reflected rayimpinges on a partially reflecting surface 264 a, which is parallel tosurface 79 a, and is coupled inside a flat prism 267, which is attachedto the upper surface 70 of the substrate 268 in a similar way that prism80 is attached to the lower surface 72 of the substrate. Thus, one wayto achieve the above is to use an air gap in the interface plane 268between the prism 267 and the substrate 258, while another way forachieving a rigid system, is to apply an optical adhesive having aproper refractive index in the interface plane 268, in order to cementthe prism 268 with the substrate 258. Part of the intensity of the lightray 260 which impinges on surface 264 a, passes through the surface asray 260 a, and continues to propagate toward the viewer's eye. Sincesurfaces 79 a and 264 a are parallel, the other part of the intensity ofthe light ray 260 is reflected from surface 264 a as ray 260 b having anoff-axis angle of α_(in) ⁽⁰⁾ and impinges again on surface 256. The rayimpinges on the surface from the left side and behaves similarly to theray that impinges on surface 65, and hence, after two reflections fromsurface 256, it propagates inside the substrate 258 having the secondorder off-axis angle of α_(in) ⁽²⁾. After two reflections from thecoupling-out surface 67, the ray 260 b is coupled out from substrate 258having the same off-axis angle α_(in) ⁽⁰⁾ and is reflected from surface79 d, which is parallel to surface 79 a, into the viewer's eye havingthe same direction as ray 260 a.

As also illustrated in FIG. 23C, another ray 262 is coupled into thesubstrate 258 after two reflections from surface 65 and propagatesinside the substrate having the second order off-axis angle of α_(in)⁽²⁾. After a few reflections from the major surfaces of the substrate258, the ray 262 impinges on surface 256. The ray impinges on thesurface from the right side and behaves similarly to the rays thatimpinge on surface 67, and hence, is coupled out from the substrate 258having an off-axis angle α_(in) ⁽⁰⁾ and is then reflected by surface 79b (or partially reflected in see-through applications), which isparallel to surface 79 a, into the viewer's eye in a similar manner toray 260. The reflected ray impinges on the partially reflecting surface264 b which is parallel to surface 79 b and 264 a and is coupled insideprism 267. Part of the intensity of the light ray 262, which impinges onsurface 264 b, passes through the surface as ray 262 a and continues topropagate toward the viewer's eye. Since surfaces 79 b and 264 b areparallel, the other part of the intensity of the light ray 260 isreflected from surface 264 b as ray 262 b having an off-axis angle ofα_(in) ⁽¹⁾, and impinges again on surface 256. The ray impinges on thesurface from the left side and behaves similarly to the ray thatimpinges on surface 65, and hence, after one reflection from surface 256it propagates inside the substrate 258 having the first order off-axisangle of α_(in) ⁽¹⁾. After one reflection from the coupling-out surface67, the ray 262 b is coupled out from substrate 258 having the sameoff-axis angle α_(in) ⁽⁰⁾ and is reflected from surface 79 c, which isparallel to surface 79 b, into the viewer's eye having the samedirection as ray 260 a. Hence, all of the four rays 260 a, 260 b, 260 aand 262 b, which originated from the same point on the display source,reach the viewer's eye having the same propagating direction.

As a result, the output aperture of substrate 258 is the combination ofsurfaces 256 and 67. Consequently, the practical active area of theoutput aperture of substrate 258 has been doubled as compared to that ofsubstrate 64, which is illustrated in FIG. 4, while the thickness of thesubstrate remains the same. On the other hand, the brightness of lightwaves coupled out from substrate 258 has been reduced as compared tothat of substrate 64. There are ways, however, to improve to brightnessof the coupled-out light waves. For embodiments wherein the light wavescoupled inside the substrate are linearly polarized, such as systemswhere the display source is an LCD or an LCOS display, the partiallyreflecting surfaces 79 i, as well as 264 i (i=a, b, . . . ), can bedesigned to be polarization-sensitive reflecting surfaces. Thesesurfaces are reflective (or partially reflective) for one polarization(preferably to s-polarization) and substantially transparent to theorthogonal polarization (preferably to p-polarization). In such a casethe transmittance of the external scene for see-through applications canbe achieved, since the entire element 255 is now substantiallytransparent to the one polarization (which is orthogonal to that of thelight waves coupled inside the substrate). While the reflecting surfaces79 i can be totally reflective for the relevant polarization (which isthe same as that of the light waves coupled inside the substrate),surfaces 254 i should be partially reflective for this polarizationwherein the exact reflection coefficient of the surfaces can bedetermined according to the number of reflecting surfaces 264 i in thesystem. For the embodiment illustrated in FIG. 23C, wherein tworeflective surfaces 256 and 67 are embedded inside the substrate 258, areflection coefficient of 0.5 can yield a total brightness efficiency of50% for the light waves coupled inside the substrate and transmittanceof 50% for the external scene.

The embodiment for expanding the output aperture by embedding areflecting surface 256 into the substrate 258, as illustrated in FIG.23C, is not limited to a single reflecting surface. An array of n flatreflecting surfaces 256 i (i=a, b . . . ), which are parallel to theoutput reflecting surface 67, can be embedded internally inside thesubstrate to increase the output aperture of the substrate by a factorof n+1. Consequently, the number of the reflecting surfaces 264 i (i=a,b . . . ) should be increased accordingly, to completely cover theoutput aperture of the embedded surfaces 256 i. The reflectance andlateral extension of each reflecting surface 264 i should be designed toensure the uniformity characteristics of the light waves coupled intothe viewer's eye.

The realization of the partially reflecting surface 198, embedded insidethe substrate 200 shown in FIG. 23A, is illustrated herein with anoptical system having the following parameters:α_(sur1)=α_(sur2)=10°; F ⁽⁰⁾={30°,40°}; F ⁽¹⁾={50°,60°} F ⁽²⁾={70°,80°};α_(sp) ⁽⁰⁾={40°,50°}; α_(sp) ⁽¹⁾={60°,70°}.  (53)

The light waves are s-polarized. The optical material of the substrate200 is Schott N-SF57 having a refractive index of n_(d)=1.846, and theoptical adhesive which is adjacent to surfaces 198 is NTT-AT9390, havingrefractive index of n_(d)=1.49, and hence, the critical angle isα_(cr)=53.5°. The reflectance of surface 198 is designed to be monotonicincreasing from 44% at α_(sp) ⁽⁰⁾=40° to 55% at α_(sp) ⁽⁰⁾=50°.

FIG. 24 illustrates the graph of the reflection from the partiallyreflecting surface 198 coated with an appropriate dielectric coating asa function of the incident angle for three different wavelengths: 450nm, 550 nm and 650 nm. As shown, the reflection is 100%, due to totalinternal reflection, for an angular spectrum of {60°, 70° }. Inaddition, the reflectance curve increases from 44% at 40° to 55% at 50°,while it is very low for the incident angles below 15°, as required.

FIGS. 5A-5D illustrate embodiments for directing the coupled-out lightwaves into the viewer's eye 24 where the light waves are reflected backby a reflecting surface 79 and pass again through the substrate 64toward the viewer's eye. An alternative way, in which the viewer's eyeis positioned at the other side of the substrate, is illustrated inFIGS. 25A-25C. As shown in FIG. 25A, four rays, 222 a, 222 b, 222 c and222 d from the same light wave, are coupled into the substrate 64 by thereflecting surface 65, and then coupled out by the surface 67 having theoff-axis angle α_(in) ⁽⁰⁾. The coupled-out light rays are reflected bythe reflecting surface 224, which is inclined at an angle

$\alpha_{ref} = {{90{^\circ}} - \frac{\alpha_{in}^{(0)}({cen})}{2}}$to the lower major surface 72 of the substrate, towards the viewer'seye. The main drawback of this embodiment is that the longitudinaldimension (along the y-axis) of the reflecting surface 224 is big,resulting in a large and cumbersome optical system.

FIG. 25B illustrates an alternative version of this embodiment in whichan array of parallel reflecting (or alternatively partially reflecting)surfaces having the same inclination angle as surface 224, is positionednext to the exit aperture of the substrate 64. The array 225 can beembedded inside a transparent prism 226 having preferably refractiveindex similar to that of the substrate 64. The optical system can now bemuch more compact than that illustrated in FIG. 25A, depending on thenumber of the reflecting surfaces in the array 225 and the thickness ofprism 226. As shown, the reflecting surfaces illustrated in FIG. 25B areadjacent to each other, i.e., the right side of each surface is adjacentto the left side of the projection of the adjacent surface. There arestill a few issues with the proposed embodiment. As shown, ray 222 b(dashed line) is reflected by the upper part of surface 225 a, which (atleast partially) prevents the continuation of the ray 222 b′ (grayarrow) from reaching the reflecting surface 225 b at point 227. As aresult, the part of surface 225 b below point 227 is blocked by surface225 a and is actually non-active (at least partially, depending on thereflectivity of surface 225 a). In addition, the presented arrangementis suitable for the central coupled-out light waves, but not for thelight waves having lower off-axis angles. As shown, the coupled-out ray228 (the part of the ray which is still coupled inside the substrate isnot shown here) having the

${{{off}\text{-}{axis}\mspace{14mu}{angle}} - \frac{FOV}{2}},$is blocked by the lower part of surface 225 c.

FIG. 25C illustrates a modified version of this embodiment in which thelower parts of the reflecting surfaces 225 which comprise the non-activeparts, are trimmed and the thickness of prism 226 is reduced,accordingly. The main outcome of this version is that the reflectingsurfaces 225 are no longer adjacent to each other. As illustrated, theintersection 230 of the coupled-out light waves with lower surface 232of prism 226 has the form of alternated dark and bright stripes. Thissignificantly reduces the performance of displays which are located at adistance from the eye, such as HUDs, wherein the stripes will benoticeably seen by the viewer's eyes, and hence, this method cannot beutilized for these applications. For near-to-eye displays, the eyeintegrates the light wave emerging from a single viewing angle andfocuses it onto one point on the retina, and since the response curve ofthe eye is logarithmic, small variations, if any, in the brightness ofthe display, will not be noticeable. Therefore, if the stripes are denseenough (namely, the lateral dimension of each stripe is significantlysmaller than the eye's pupil), and if the eye is positioned close enoughto the substrate, the viewer can still experience a high-quality imageeven with the stripes. Moreover, the active area of the reflectingsurfaces 225 can be further trimmed to yield a lower fill-factor of theilluminated areas on surface 232. While the projection 230 of thereflecting surfaces 225 on surface 232 are the areas in which thecoupled-out light waves of the projected image pass through towards theviewer's eye, the other non-illuminated areas 234 are the “slits” wherethe light waves from the external scene can pass through toward the eye,for see-through applications. Consequently, the ratio between thebrightness of the projected image and that of the external scene can becontrolled by setting the proper fill-factor of the projected areas 230,accordingly. In addition, the reflectance of the reflecting surfaces 225can be materialized by applying to the surfaces an optical adhesivehaving refractive index which is lower than that of the prism 226, suchthat the oblique angles of incident of the coupled-out light waves onthe reflecting surfaces 225 will be higher than the critical angle toyield total internal reflection of the light waves from the surfaces.The “trimmed array” embodiment illustrated in FIG. 25C, deflecting thecoupled-out light into the viewer's eye, can also be applied to theembodiments illustrated in FIG. 5C. This means that the reflectingsurfaces 79 i (i=a, b . . . ) will no longer be located adjacent to eachother, and the ratio between the brightness of the projected image andthat of the external scene will be determined by setting the properfill-factor of the reflecting surfaces 79 i in the prism 80, as well asby setting the reflectance of surfaces 79 i. In addition, the “trimmedarray” embodiment can also be applied to the multi-reflecting surfacesembodiment illustrated in FIG. 23C. That is to say, the reflectingsurfaces 264 i (i=a, b . . . ) will no longer be adjacent to each other,and the ratio between the brightness of the light waves passing thoughthe reflecting surfaces 264 i to reach the viewer's eye and the lightwaves which are reflected by these surfaces to be coupled again into thesubstrate, will be determined by setting the proper fill-factor of thereflecting surfaces 264 i in the prism 267, as well as by setting thereflectance of surfaces 264 i.

The re-directing embodiment illustrated in FIGS. 25B and 25C is mainlyappropriate for embodiments where the coupling-out surfaces are totallyreflecting. For embodiments such as those illustrated in FIGS. 23A and23B, where part of the coupling-out elements are partially reflectingsurfaces, care must be taken that light waves from the external scenewill not penetrate the partially reflecting surface 200, be reflected bysurfaces 225 into the viewer's eye, and hence, create a ghost image.

In all the embodiments illustrated hereinabove, it was assumed thatlight waves having only the first and the second orders of axis-axisangles, propagate inside the substrate. There are systems, however,having comparatively small FOVs, where even the third order can beutilized. Referring to FIG. 5C and assuming, for example, an opticalsystem having the following parameters:α_(sur1)=α_(sur2)=9°; F ⁽⁰⁾={18°,27°}; F ⁽¹⁾={36°,45°} F ⁽²⁾={54°,63°};F ⁽³⁾={72°,81°}  (54)where the light waves are s-polarized, the optical material of thesubstrate is Schott N-SF57 having a refractive index of n_(d)=1.846, andthe optical adhesive which is used to cement the substrate 64 to theprism 80 is NTT-E3337 having refractive index of n_(d)=1.42, wherein theinterface plane 83 (FIG. 5D) between substrate 64 and prism 80 coversthe entire lower major surface 72. The critical angle of the lowersurface is therefore α_(cr) ^(l)=50.3. The interface between thesubstrate and the collimating element of the input light waves is an airgap and the critical angle of the upper surface is therefore α_(cr)^(u)=32.8. All of the optical rays in the higher orders of F⁽²⁾ and F⁽³⁾have off-axis angles higher than the critical angles and they aretherefore totally reflected from the interface plane 83, as well as fromthe upper surface 70. In addition, the light waves in the first orderare totally reflected from the upper surface 70, and hence, they can beused to create the second and the third orders during the coupling-inprocess. On the other hand, all the optical rays in the first orderimpinge on the interface plane 83 at an incident angle lower than thecritical angle there, and hence, they cannot propagate inside thesubstrate by total internal reflection. In addition, during thecoupling-out process the light waves which are transferred to the firstorder by the reflections of the higher orders from surface 67 passthrough the interface plane 83 and are coupled out from the substrate 64as the output light waves by the coupling-out element 67. The inputlight waves are in the zero order of F⁽⁰⁾, the output light waves are inthe first order of F⁽¹⁾ while the light waves that propagate inside thesubstrate are in the higher orders of F⁽²⁾ and F⁽³⁾. Consequently, sincethe width of the input light waves required to create the higher ordersis much narrower than that of the coupled-out first order, the actualinput aperture of the system will be substantially smaller that theoutput aperture.

As illustrated in FIG. 26, an input ray 250 impinges on substrate 64having an off-axis angle α_(in) ⁽⁰⁾. After three reflections fromsurface 65 at points 252 a, 252 b and 252 c, this ray is coupled insidethe substrate and propagates inside it having the third order off-axisangle of α_(in) ⁽³⁾. After a few reflections from the major surfaces ofthe substrate 64, the ray 250 impinges on surface 67. After tworeflections from the surface at points 254 a and 254 b it is coupled outfrom the substrate 64 having an off-axis angle α_(in) ⁽¹⁾. The light ray250 is then reflected by surface 79 a, substantially normal to thesubstrate's major surface into the viewer's eye 24.

FIGS. 27a and 27b illustrate a method for fabricating the requiredtransparent substrates. First, a group of prisms 236 is manufactured,having the required dimensions. These prisms can be fabricated fromsilicate-based materials, such as Schott SF-57 with the conventionaltechniques of grinding and polishing, or alternatively, they can be madeof polymer or sol-gel materials using injection-molding or castingtechniques. The appropriate surfaces of these prisms are then coatedwith the required optical coatings 237. Finally, the prisms are gluedtogether to form the desired substrate 238. In applications in which thequality of the optical surfaces is critical, the final step of polishingthe outer surfaces, or at least part of them, can be added to theprocess.

FIGS. 28a-28e illustrate another method for fabricating the transparentsubstrates. A plurality of transparent flat plates 239 coated with theappropriate optical coatings 240 step (a) (if required) are cementedtogether using the appropriate optical adhesives so as to create astacked form 242 step (b). A number of segments 244 step (c) are thensliced off the stacked form by cutting, grinding and polishing, tocreate the desired substrates 246 step (d). Several elements 248 can becut-off from each slice 246, as shown by a top view of step (e). FIGS.27 and 28 illustrate methods for fabricating substrates having only tworeflecting surfaces. For other embodiments, such as those illustrated inFIG. 12 or 23, where other reflecting surfaces are embedded inside thesubstrates, a larger number of prisms (FIG. 27) or flat plates (FIG. 28)should be added to the fabrication process accordingly.

FIGS. 5-26 illustrate various features which can be added to the basicconfiguration illustrated in FIGS. 4A-4B, including: various types offolding reflecting surfaces (FIGS. 5 and 25); external correcting lenses(FIGS. 8A-8C); blocking of the non-active part of the coupling-outelements (FIGS. 9A-9C); a special compensation design (FIG. 9D);combining of a few substrate together (FIGS. 11, 18, 20 and 23B);embedding an angular sensitive reflecting surface in the substrate forreducing the input aperture (FIGS. 12A-12B) or for mixing the coupled-inlight waves (FIGS. 12C-12D); adding different coupling-in elements(FIGS. 15A-15B); cementing a thin transparent plate to one (or more) ofthe major surfaces of the substrate to mix the coupled-in light waves(FIGS. 16B-16C); utilizing angular sensitive coupling-in surfaces forincreasing the brightness of the optical system (FIGS. 18 and 20);embedding partially reflecting surfaces inside the substrate or next tothe major surfaces of the substrate to increase the output aperture of asingle substrate (FIGS. 23A-23C) and using more than two propagationorders of the coupled light waves inside the substrate (FIG. 26).Eventually, any combination of any number of these features can be addedtogether to the basic embodiment which is illustrated in FIGS. 4A-4B,according to the specific requirements of the optical system.

It will be evident to those skilled in the art that the invention is notlimited to the details of the foregoing illustrated embodiments and thatthe present invention may be embodied in other specific forms withoutdeparting from the spirit or essential attributes thereof. The presentembodiments are therefore to be considered in all respects asillustrative and not restrictive, the scope of the invention beingindicated by the appended claims rather than by the foregoingdescription, and all changes which come within the meaning and range ofequivalency of the claims are therefore intended to be embraced therein.

What is claimed is:
 1. A method for fabricating an optical device havinga light wave transmitting substrate with at least two major surfaces andedges, and input and output reflecting surfaces carried by thesubstrate, for producing a substrate allowing light waves to traversethe substrate between the two major surfaces, the method comprising:attaching to each other a plurality of flat plates arranged in a stack;slicing the stack to form a substrate with two major surfaces, acoupling-in reflecting surface and a coupling-out reflecting surface,with the major surfaces being parallel to each other and not parallel tothe input or the output surfaces; grinding or polishing the substrate;and cutting the substrate to final dimensions,. wherein all the flatplates in the stack are substantially entirely transparent.
 2. Themethod as claimed in claim 1, wherein each of the flat plates has twomain surfaces parallel to each other.
 3. The method as claimed in claim2, wherein at least one of the main surfaces of the flat plates iscoated with an anti-reflecting coating.
 4. The method as claimed inclaim 1, wherein all the flat plates are substantially transparent tonormally incident visible light.
 5. The method as claimed in claim 2,wherein all the flat plates are substantially transparent for the lightwaves impinging on the main surfaces having incidence angles smallerthan their critical angle.
 6. The method as claimed in claim 1, whereinall the flat plates have the same refractive index.
 7. The method asclaimed in claim 1, wherein the flat plates are attached to each otherby an optical adhesive, the refractive index of the optical adhesivebeing substantially lower than the refractive index of the plates. 8.The method as claimed in claim 1, further comprising cementing anoptical means to one of the major surfaces of the substrate forredirecting coupled-out light waves from the substrate into a viewer'seye.
 9. The method as claimed in claim 1, further comprising cementingan optical means to the substrate for coupling light into the substrateby total internal reflection.
 10. The method as claimed in claim 1,wherein at least two segments are sliced off from the stack.
 11. Themethod as claimed in claim 1, wherein the substrate is substantiallytransparent to normal incident visible light.
 12. The method as claimedin claim 1, wherein at least one of the major surfaces of the substrateis coated with an anti-reflection coating.
 13. The method as claimed inclaim 1, wherein the substrate is substantially transparent for thelight waves impinging on the major surfaces having incidence anglessmaller than the critical angle.
 14. The method as claimed in claim 1,wherein the substrate is substantially transparent for the light wavesimpinging on the coupling-out reflecting surface having incidence anglessmaller than the critical angle.
 15. The method as claimed in claim 1,wherein the substrate is substantially transparent for light wavesimpinging on the coupling-in reflecting surface having incidence anglessmaller than the critical angle.
 16. The method as claimed in claim 1,wherein the transparent flat plates are arranged in a staggered stack.17. A method for fabricating an optical device having a light-wavetransmitting substrate with at least two major surfaces and edges, andinput and output reflecting surfaces carried by the substrate, forproducing a substrate allowing light-waves to traverse the substratebetween the two major surfaces, the method comprising: attaching to eachother a plurality of substantially entirely transparent flat platesarranged in a stack; slicing the stack to form a substrate with twomajor surfaces, a coupling-in reflecting surface and a coupling-outreflecting surface, the major surfaces being parallel to each other andnot parallel to the input or the output surfaces; grinding or polishingthe substrate; and cutting the substrate to a final dimension, whereinall the transparent flat plates are uninterruptably cemented to eachother.